Logarithms€¦ · 19/10/2020 · 2 3 Subtract Logarithms.....1215 2 4 Fraction Logs.....1344 2 5...
Transcript of Logarithms€¦ · 19/10/2020 · 2 3 Subtract Logarithms.....1215 2 4 Fraction Logs.....1344 2 5...
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Logarithms
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1 1 Exponents.................................5
1 2 Logarithm Form....................168
1 3 Change Exponent to Logs...351
1 4 Decimals 2/4 and 3/6............460
1 5 Decimals 7, 8, 9, and 5.........634
1 6 Go Backwards......................778
2 1 Add Logarithms....................884
2 2 Carry Logarithms................1051
2 3 Subtract Logarithms..........1215
2 4 Fraction Logs......................1344
2 5 Fractions Less Than 1........1499
2 6 Logs of Decimals................1654
Log
Add
Subtract
and
Fractions
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3 1 Logs for 2 Digit Numbers......1774
3 2 Logs for Scientific Notation..1959
3 3 Power Logarithms.................2076
3 4 Radical Logarithms...............2237
4 1 Other Bases Logarithms.......2403
4 2 Change to Other Bases.........2497
4 3 Exponential Equations..........2642
4 4 Same Base Equations...........2820
5 1 Log Equations.......................2967
5 2 Antilogarithms.......................3066
5 3 Take Log of Both Sides........3231
Other
Bases
and
Equations
Equations
With Logs
2 Digit
and
Power
Logs
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5 4 Equations With MA Rule....3453
5 5 Fraction Logarithms..........3641
6 1 Natural Numbers................3797
6 2 Continuous Growth Logs..3981
6 3 Natural Logarithms............4157
7 1 Earthquakes.......................4360
7 2 Compare Earthquakes.......4561
7 3 pH Levels............................4678
7 4 Sound..................................4862
Word
Problems
Natural
Logs
0004
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0005
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1. What do logarithms find...................62. Exponents with different bases......623. Questions 1..................................1004. Questions 2..................................1205. Performance 1.............................1406. Performance 2.............................154
Chapter 1 Lesson 1Basic Logarithms
0006
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Adjust your screen for correct lettering.
Chapter 1 Lesson 1
Basic Logarithms
What do logarithms find?
0007
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Logarithm sounds like a log has rhythm.
Logarithm
0008
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Sorry, no trees playing drums here, although that is funny.
0009
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Well, I'm not the one who came up with a crazy name.
0010
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True. I don't know who named it, but it's a new way to write numbers.
What does an exponent do?
0011
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10 2 ExponentBase
The exponent shows how many times to multiply the base.
0012
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Ok, what does it equal?
10 2 ExponentBase
0013
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10 = 1002
Cheezy. That equals 100.
0014
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10 = 1002
Yeah, but what's the name forit? I came up with a name myself.
0015
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10 = 1002
Real Number
Why is it called Real Number?
0016
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10 = 1002
Real Number
It needed a name, just like base and exponent. It's a real number.
Lots to do. Time to move on.
0017
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So, what do logarithms do?
Logarithms
0018
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Scientific notation is one way of writing numbers.
Logarithms is another step.
0019
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Big step or little step?
0020
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Now you can write any number by it's exponent.
Very Big.
0021
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Ummm, you just said that.
0022
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True. And that's how big this idea is. I'll explain it.
0023
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10 2
You know, we already use numbers to write exponents.
0024
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Yeah, that's the 1st step to it. I'll write it in bigger words.
0025
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I t finds exponents.
I still have no idea.
0026
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Instead of thinking about 100as the number, think of the 2.
I'll show you what I mean.
0027
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You already know 2 is the exponent that makes 100.
10 = 1002
0028
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We've done that like 10 times.
10 = 1002
0029
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So, if I make the exponenta 3, what's the real number?
10 = ?3
0030
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Now the real number is 1000.
10 = 10003
0031
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I'll make a chart to show it.
The exponent counts the places.
10 = 10003
0032
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10 100 210 1000 3
Base Real Number Exponent
Ok, I see what it makes.
0033
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10 100 210 1000 3
Base Real Number Exponent
We'll see. I'll add another one.
0034
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10 100 210 1000 3
4
Base Real Number Exponent
That's all there is? Just 4?
0035
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10 100 210 1000 3
4
Base Real Number Exponent
What real number with base 10 makes it 4?
0036
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10 = 10,0004
That's 10,000, because there's 4 places.
0037
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10 = 10,0004
That's how to think of numbers as their exponents. Think about it.
0038
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10 100 210 1000 3
2 and 3 are the number.
Base Real Number Exponent
0039
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10 100 210 1000 3
You do need the base.Here's a problem with it.
Base Real Number Exponent
0040
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10 x 102
What's 10 squared x 10 cubed?
3
0041
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10 x 102
That's a really old problem. Just use the MA Rule.
3
0042
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10 x 10 = 102
Add 2 + 3 is 5, so 10 to the 5th.
3 5
0043
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10 x 10 = 102
I'll change the exponents.
3 5
0044
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10 x 103
Instead of 2, it's a 3. What does it equal?
3
0045
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10 x 103
But, it's a different problem.Another easy one. I know it.
3
0046
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10 x 10 = 103 3 6
So, add them.10 to the 6th is 1,000,000.
0047
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10 x 10 = 103 3 6
So, what changed and what told you what the number was?
0048
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10 x 10 = 103 3 610 x 10 = 102 3 5
The exponent is what changed.
0049
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10 x 10 = 103 3 610 x 10 = 102 3 5
That's why it works. Theexponent told you the number.
0050
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So, this log thing is going to change everything?
0051
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Pretty much true. It will be totally different.
0052
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10 = 1002
What are the names for the numbers in exponent form?
Qs
0053
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10 = 1002 Real Number
Exponent
Base
Base to the exponent equals a real number.
0054
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What does a logarithm do?
0055
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I t finds exponents.
The exponent is the main number.
0056
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10 2
What does the exponent on base 10 show you?
0057
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10 = 1002
2 counts the zeros.
Place Value
0058
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How does changing the exponent change the numbers?
10 5 10 2
0059
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10 = 100,00051 2 3 4 5
Change the exponentchanges the real number.
10 = 10021 2
(Along with the base.)
0060
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0061
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Chapter 1 Lesson 1
Basic Logarithms
Exponents with different bases.
0062
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Does all this use different bases besides 10?
0063
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Good question, becausebases is what made it happen.
I'll go over different bases.
0064
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10 = 10003
If we change the base to another number then it willmake a different real number.
I'll change it to a 2.
0065
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2 = 83
Wow! Big difference.
0066
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2 = 83
Same exponent, but the base number gives a different answer.
Here's a different one.
0067
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5 = 252
You know 5 squared is 25.
What happens when you change the exponent to a 3?
0068
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5 = 1253
Changing the exponent really changes the real number.
0069
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5 = 1253
There is a word for that.
0070
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Exponential
Duh. It's got the word exponent in it.
0071
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If you have a stock worth Rs 25one day and it's Rs 125 the next...
0072
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5 = 1253
That would be alot of money.
0073
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5 = 1253
I don't think you get it. The next morning you wake up and...
0074
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5 = 6254
Rs 625?! Yeah, I would love that.
0075
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Remember, this is algebra.
The pow er of exponents.
0076
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What do you mean,"algebra"? I thought it was algebra 2.
0077
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Algebra in general. Thatmeans we need variables.
I'll make 1 so you can see it.
0078
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2 = x3
Wow. That is a tough problem. Not really.
0079
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2 = x3
Take your time. How do you solve it?
0080
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2 = x 8 = x
3
Duh, 2 x 2 x 2 equals 8.
0081
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Very good. I'll change the exponent.
0082
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2 = x3.7
I was kidding last time. This is a tough problem.
0083
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2 = 133.7
Logarithms can solve that. I'll move the variable.
0084
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2 = 16x
Now X is the exponent.
0085
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2 = 16x
How do you solve for X?
0086
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2 = 16x
Does it count if I know the answer?
0087
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2 = 16x
Alittle. What is the answer?
0088
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2 = 164
X is 4, because 2 x 2 is 4 and 4 x 4 is 16.
0089
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I'll change it alittle.
Here's another problem.
0090
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10 = 20x
Nope. Don't know that one either
0091
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10 = 201.3
Again. Logarithms will solve that.
0092
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Logarithms
I'm guessing that logarithms is alot tougher than I thought.
0093
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I guarantee that you willlearn more about exponents.
0094
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Is that a money back guarantee?
0095
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Sure, if I had any. Trust me. You will learn exponents.
0096
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Qs
10 2
Why is the base important?
5 2
0097
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5 = 252
Different base numbers make a different real number.
10 = 1002
0098
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0099
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Practice #1
Chapter 1 Lesson 1
Basic Logarithms
How logarithms use exponents.
0100
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What are the names for the numbers in exponent form?
10 = 100212 3
0101
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10 = 1002Base
Exponent
Real Number
Base to the exponent equals the real number.
0102
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What does a logarithm do?
0103
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I t finds exponents.
The exponent is the main number.
0104
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How does changing the exponent change the numbers?
10 5 10 2
0105
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10 = 100,00051 2 3 4 5
Change the exponentchanges the real number.
10 = 10021 2
(Along with the base.)
0106
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10 2
What does the exponent 2 on base 10 show you?
0107
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10 = 1002
2 counts the zeros
0108
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10 = 1000x
What exponent solves base 10 equals 1000?
Problems
0109
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10 = 10003
It's 3. 10 to the 3rd is 1000.
0110
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What exponent solves base 10 equals 1 million?
10 = 1,000,000x
0111
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10 = 1,000,0006
6 because there's 6 places in 1,000,000.
0112
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10 = ?4
10 to the 4th makes what number?
0113
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10 = 10,0004
10 to the 4th is 10 thousand.
0114
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2 = ?4
What are 2 to the 4th and 6th?
2 = ?6
0115
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2 = 164
2 to the 4th is 16 and 2 to the 6th is 64.
2 = 646
0116
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5 = ?2
What is 5 squared and cubed?
5 = ?3
0117
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5 = 252
5 squared is 25 and 5 to the 3rd is 125.
5 = 1253
0118
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0119
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Practice #2
Chapter 1 Lesson 1
Basic Logarithms
How logarithms use exponents.
0120
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What are the names for the numbers in exponent form?
10 = 100212 3
0121
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10 = 1002Base
Exponent
Real Number
Base to the exponent equals the real number.
0122
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What does a logarithm do?
0123
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I t finds exponents.
The exponent is the main number.
0124
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How does changing the exponent change the numbers?
10 5 10 2
0125
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10 = 100,00051 2 3 4 5
Change the exponentchanges the real number.
10 = 10021 2
(Along with the base.)
0126
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What does the exponent 2 on base 10 show you?
10 2
0127
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10 = 1002
2 counts the zeros
0128
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10 = 100x
What exponent solves base 10 equals 100?
Problems
0129
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10 = 1002
It's 2. 10 squared is 1000.
0130
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What exponent solves base 10 equals 10 million?
10 = 10,000,000x
0131
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10 = 10,000,0007
7 because there's 7 places in 10 million.
0132
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10 = ?5
10 to the 5th makes what number?
0133
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10 = 100,0005
10 to the 5th is 100 thousand.
0134
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3 = ?3
What are 3 cubed and to the 4th?
3 = ?4
0135
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3 = 273 3 = 814
3 cubed is 27and 3 to the 4th is 81.
0136
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2 = ?3
What is 2 cubed and 2 to the 4th?
2 = ?4
0137
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2 = 83 2 = 164
2 cubed is 8 and to the 4th is 16.
0138
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0139
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Performance #1
Chapter 1 Lesson 1
Basic Logarithms
How logarithms use exponents.
0140
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10 = 1000x
Find the exponents.
10 = 10,000x
0141
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10 = 1000
10 = 10,0004
3
1000 is cubed and 10,000 is 4th.
0142
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10 = 1,000,000x
Find the exponents.
10 = 10,000,000x
0143
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10 = 1,000,0006
10 to the 6th is 1 million and10 to the 7th is 10 million.
10 = 10,000,0007
0144
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10 = x9
10 = x10
What is 10 to the 9th and 10th?
0145
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1,000,000,000
10,000,000,000
10 = 9
10 = 10
0146
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10 = x1
10 = x0
What is 10 to the 1st and 0 power?
0147
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10 = 101
10 = 10
10 to the 1st is 10 and any number to the 0 power is 1.
0148
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2 = ?4
What are 2 to the 4th and 6th?
2 = ?6
0149
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2 = 164
2 to the 4th is 16 and 2 to the 6th is 64.
2 = 646
0150
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5 = ?3
What are 5 to the 3rd and 4th?
5 = ?4
0151
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5 = 1253 5 = 6254
5 to the 3rd is 125 and 5 to the 4th is 625.
0152
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0153
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Performance #2
Chapter 1 Lesson 1
Basic Logarithms
How logarithms use exponents.
0154
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10 = 100x
Find the exponents.
10 = 100,000x
0155
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10 = 100
10 = 100,0005
2
100 is squared and 100,000 is 5th.
0156
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10 = 100,000,000x
Find the exponents.
10 = 1,000,000,000x
0157
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10 = 100,000,000
10 = 1,000,000,000
8
10 to the 8th is 100 million and10 to the 9th is 1 billion.
9
0158
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10 = x10
10 = x11
What is 10 to the 10th and 11th?
0159
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10,000,000,000
100,000,000,000
10 = 10
10 = 11
10 to the 10th is 10 billion and10 to the 11th is 100 billion.
0160
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10 = x3
10 = x0
What is 10 to the 3rd and 0 power?
0161
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10 = 10003
10 = 10
10 to the 3rd is 1000 and any number to the 0 power is 1.
0162
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2 = ?3
What are 2 to the 3rd and 5th?
2 = ?5
0163
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2 = ?3 2 = ?5
2 to the 3rd is 8 and 2 to the 5th is 32.
0164
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3 = ?3
What are 3 to the 3rd and 4th?
3 = ?4
0165
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3 = 273 3 = 814
3 to the 3rd is 27 and 3 to the 4th is 81.
0166
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0167
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1. What do logarithms look like?..1682. How to say a logarithm............2273. Questions 1.............................2834. Questions 2.............................3055. Performance 1........................3236. Performance 2........................337
Chapter 1 Lesson 2Basic Logarithms
0168
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Adjust your screen for correct lettering.
Chapter 1 Lesson 2
Basic Logarithms
What do logarithms look like?
0169
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So, when do I get to see what a logarithm looks like?
0170
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Your wish is my command. I'll show you the left side.
0171
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log 100 10
Does log mean logarithm?
0172
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log 100 10
Yup. The base is a little number and the real number is next to it.
Watch where the exponent goes.
base
real number
0173
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log 100 = 210
It equals the exponent?
Exponent
0174
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log 100 = 210
The exponent is what's important. Where is the base number at?
Exponent
0175
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log 100 = 210
Base is the little number under it.
Base
0176
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log 100 = 210
Right. Where does it go to get the exponent?
Base
0177
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log 100 = 210
Up the slide. That's 10 squared.
0178
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log 100 = 210
Where is the real number at?
0179
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log 100 = 210
Go across to the real number.
0180
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log 100 = 210
That's the logarithm form.What number does it look like?
0181
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log 100 = 210
It looks like the number 7 .
7
0182
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log 100 = 210
7 shows how it works. I'll get another problem.
0183
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log 1000 10
Alot like the last one.
0184
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log 100010
Ok, what's the exponent here?
0185
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log 1000 = 310
How did you know that?
0186
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log 1000 = 310
I'll show you how to count place values.
0187
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1 , 0 0 01 2 3
Count the places to the 1st digit.
0188
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So, the exponent is 3?
1 , 0 0 01 2 3
Ok, I get how that works.
0189
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log 1000 = 310
Yes. Where does it start to find the exponent form?
0190
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log 1000 = 310
Start at the base 10 and slide upto the 3.
0191
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log 1000 = 310
Where does it go from there?
0192
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log 1000 = 310
Go across to finish the 7.
0193
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log 1000 = 310
So, what's the exponent form?
0194
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10 to the 3rd makes 1000.
10 10003 =
0195
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10 10003
10 to the 3rd power is 1000.
=
log 1000 = 310
0196
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10 = 10,000?
Think about how you get the exponent for 10,000, base 10.
0197
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1 0 , 0 0 01 2 3 4
Count the places to after the 1st digit.
0198
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1 0 , 0 0 01 2 3 4
So, what's the exponent?
0199
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10 = 10,0004
Easy enough. It's 4.Make a chart for it.
0200
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log 10 = 1log 100 = 2log 1000 = 3log 10,000 = 4
The exponent shows the place value part to the real number.
0201
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1 x 10 5
When you look at scientificnotation, it's the exponent on 10.
That's how scientific notation is alot like logarithms. What's this one?
0202
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1 0 0 ,0 0 01 2 3 4 5
10
So, the exponent would be 5.
is5
0203
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1 0 0 ,0 0 01 2 3 4 5
10is 5
Good!! I'll go over a few to see if you make exponent form.
0204
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log 10 = x10
One very nice logarithm.What's the exponent here?
0205
-
log 10 = x10
10 has just 1 zero, so it's a 1.
0206
-
log 10 = 110
Right. What's the exponent form?
0207
-
log 10 = 110
First, start at the base. I'll show you.
0208
-
log 10 = 110
Upto the exponent and across to the real number.
0209
-
log 10 = 110
What's the exponent form?
0210
-
log 10 = 110
The exponent is 10 to the 1st.
10 = 101
0211
-
log 10 = 110
That's what you think about.Exponent form starts at the base.
10 = 101
One more...
0212
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log 1 ,000,000 = 610
Last one.What's the exponent form?
0213
-
log 1 ,000,000 = 610
It's six. Ok, I think I see it now.
0214
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log 1 ,000,000 = 610
10 to the 6th is 1 million.
10 = 1,000,0006
0215
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The next lesson is important.
0216
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Qs
log 100 = ?10
What do logarithms equal?
0217
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log 100 = 210
Logs equal the exponent.
0218
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Where is the base in a logarithm?
log 100 = 210
0219
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log 100 = 210
Base
Base is the lit t le number.We don't always write it if it's 10.
0220
-
Where does it start to change log to exponent form?
log 100 = 210
0221
-
What shape shows how to change it?
log 100 = 210
Start at the base number.
0222
-
10 squared is 100.
log 100 = 210
Think of a 7 .
0223
-
log x = 310
If we change the log exponent to a 3, what does it change?
0224
-
log 1000 = 310
Real Number is 1000. Change the exponent changes the real number.
0225
-
0226
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Chapter 1 Lesson 2
Basic Logarithms
How to say a logarithm.
0227
-
Before we go any further, I need to go over how to say them.
Say a logarithm.
0228
-
How to say them? That's too easy.
0229
-
log 100 = 210
Ok, how do you say this log?
0230
-
log 100 = 210
Ummm, probably log of something something something.
0231
-
Say Logarithm of 100, base 10, is 2.
log 100 = 210
Just look for the checkmark.
0232
-
log 100 = 210
What checkmark is that?
0233
-
That starts the checkmark.
log 100 = 210
Start with Log of 100.
0234
-
log 100 = 210
Go to Base 10. That's the bottom of the checkmark.
0235
-
The log exponent is the end of the checkmark.
log 100 = 210
Finish at is 2 .
I'll change the problem.
0236
-
log 10 = 110
How do you say this one?
0237
-
log 10 = 110
Can you show me the checkmark?
0238
-
log 10 = 110
Remember where it starts.
0239
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log 10 = 110
I know the 1st part is Log of 10.Ok, here it is...
0240
-
It's Logarithm of 10 base 10 is 1.
log 10 = 110
0241
-
I've got one more.
Work on the middle part.
0242
-
log 1000 = 310
Start with log of 1000.
Here's the rest.
0243
-
It's Logarithm of 1000 base 10 is 3.
10log 1000 = 3
I know this one.
0244
-
I'll make initials for it so you can remember it.
0245
-
What does that tell me?
RBE
0246
-
Real number to the base to the exponent or...
0247
-
I think I'll use the checkmark.
Checkmark
0248
-
At least you know how to say it now.
0249
-
I know logarithms are important, but do we really use it for anything?
0250
-
Good point. No use learning something we'll never use.
0251
-
How about earthquakes? Are they important?
0252
-
Great day!! They destroy buildings and everything.
0253
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They use logarithms.How about how loud a sound is?
0254
-
I know. You're going to tellme they use logarithms, too.
0255
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Both earthquakes and sounduse logarithms to measure them.
Sound
0256
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Anything else I might need?
0257
-
Is that like the PH on phone?
PH Levels
0258
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It's how acid or basesomething is. It uses logs.
Say each one, P, then H.
0259
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Don't tell me the Rule of 3s uses logarithms too?
Rule of 3s
0260
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The opposite way around.Logarithms use the Rule of 3s.
0261
-
How do logarithms do that?
0262
-
Relax. This makes it easier to figure out. I'll show you.
0263
-
What's this real number?
log ? = 6
0264
-
log 1,000,000 = 6
Log of a million is 6.
Am I right?
0265
-
log 1,000,000 = 6
Uhhh, you forgot the base 10 part.
0266
-
log 1,000,000 = 6
You didn't write it in there,so I figured it wasn't important.
0267
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log 1,000,000 = 6
We use base 10 so muchthat you don't have to write it, but you still have to say it.
0268
-
log 1,000,000 = 6
Hey, less writing for me.
0269
-
log 1,000,000 = 6
There's 6 places in millions. That's the Rule of 3s.
0270
-
log 1,000,000 = 6
Ok, I'll make the next one.
0271
-
log ? = 7
That would add 1 more. All the 10s use it.
I've got that together.
0272
-
log 10,000,000 = 7
6 places in million's place,so add 1 more to get 10s.
1 more thing to show you.
0273
-
2 = log 10010
Hey, it's backwards.
0274
-
Some books write the logarithm backwards.
2 = log 10010
Same stuff. Nothing changes.
0275
-
Qs
log 100 = 2 10
Where do you start to say a log?
0276
-
log 100 = 210
Start with Log of 100.
0277
-
log 100 = 210
What shape does saying a log use?
0278
-
log 100 = 210
Checkmark
Say Logarithm of 100, base 10, is 2.
0279
-
log 10,000 = 410
How do you say this logarithm?
0280
-
log 10,000 = 410
Say Logarithm of 10,000, base 10, is 4.
Start at log 10,000.
0281
-
0282
-
Practice #1
Chapter 1 Lesson 2
Basic Logarithms
Name 3 parts to logarithms and how to say them.
0283
-
What do logarithms equal?
log 100 = ?10
0284
-
log 100 = 210
ExponentReal Number
Logarithms equal the exponent. Where is the base in a logarithm?
0285
-
log 100 = 210
Base
Base is the lit t le number.We don't always write it if it's 10.
0286
-
Where does it start to change log to exponent form?
log 100 = 210
0287
-
What shape shows how to change it?
log 100 = 210
Start at the base number.
0288
-
10 squared is 100.
log 100 = 210
Think of a 7 .
0289
-
log x = 310
If we change the log exponent to a 3, what does it change?
0290
-
log 1000 = 310
Real Number is 1000. Change the exponent changes the real number.
0291
-
Problems
log 10,000 = x10
How does log of 10,000, base 10, show you the exponent?
0292
-
log 10,000 = x10
How does it make the exponent?
Look at the real number.
0293
-
log 10,000 = 410
So the log exponent is 4.
I t has 4 zeros.
0294
-
log 1000 = 310
What's the 1st step to change log to exponent form?
0295
-
10 3
log 1000 = 310
10 cubed pow er.Start at the base.
How do you finish it?
0296
-
10 = 1,0003
log 1000 = 410
10 to the 3rd power is 1,000.
Go across to the real number.
0297
-
log 100,000,000 = x10
What is the log exponentfor log of 100 million, base 10?
0298
-
log 100,000,000 = 810
What is the exponent form?
Log of 100 million, base 10, is 8 .
0299
-
10 = 100,000,0008
log 100,000,000 = 810
10 to the 8th is 100 million.
0300
-
log x = 610
What is the real number for base 10 to the 6th?
0301
-
What is the exponent form?
Logarithm of 1 ,000,000, base 10, is 6 .
log 1 ,000,000 = 610
0302
-
10 = 1,000,0006
log 1,000,000 = 610
10 to the 6th is 1 million.
0303
-
0304
-
Practice #2
Chapter 1 Lesson 2
Basic Logarithms
Name 3 parts to logarithms and how to say them.
0305
-
Qs
log 100 = 2 10
Where do you start to say a log?
0306
-
log 100 = 210
Start with Log of 100.
0307
-
log 100 = 210
What shape does saying a log use?
0308
-
log 100 = 210
Checkmark
Say Logarithm of 100, base 10, is 2.
0309
-
Problems
log 100,000 = x10
How does log of 100,000, base 10, show you the exponent?
0310
-
log 100,000 = x10
How does it make the exponent?
Look at the real number.
0311
-
log 100,000 = 510
So the log exponent is 5.
I t has 5 zeros.
0312
-
log 100 = 210
What's the 1st step to change log to exponent form?
0313
-
10 2
log 100 = 210
10 squared.Start at the base.
How do you finish it?
0314
-
10 = 1002
log 100 = 310
10 squared is 100.
Go across to the real number.
0315
-
log 1,000,000,000 = x10
What is the log exponentfor log of 1 billion, base 10?
0316
-
log 1,000,000,000 = 910
What is the exponent form?
Log of 1 billion, base 10, is 9 .
0317
-
10 = 1,000,000,0009
log 1,000,000,000 = 910
10 to the 9th is 1 billion.
0318
-
log x = 710
What is the real number for base 10 to the 7th?
0319
-
What is the exponent form?
Logarithm of 10 million base 10, is 7 .
log 10,000,000 = 710
0320
-
10 = 10,000,0007
log 10,000,000 = 710
10 to the 7th is 10 million.
0321
-
0322
-
Performance #1
Chapter 1 Lesson 2
Basic Logarithms
Name 3 parts to logarithms and how to say them.
0323
-
log 10,000 = x10
What exponent goes with each logarithm?
log 100,000 = x10
0324
-
log 10,000 = 410
log 100,000 = 510
10,000 is 4 and 100,000 is 5.
0325
-
log 10 = x10
What exponent goes with each logarithm?
log 1 = x10
0326
-
10 is 1 and 1 is 0.
log 10 = 110
log 1 = 010
0327
-
Find the real numbers.
log x = 5
log x = 4
0328
-
log 100,000 = 5
log 10,000 = 4
5 is 100 thousand and 4 is 10 thousand.
0329
-
Find the real numbers.
log x = 6
log x = 8
0330
-
6 is 1 million and 8 is 100 million.
log 1,000,000 = 6
log 100,000,000 = 8
0331
-
log 10,000 = 410
Change this log to exponent form.
0332
-
10 10,0004 =
log 10,000 = 410
10 to the 4th is 10,000.
0333
-
Change this log to exponent form.
log 100 = 210
0334
-
10 squared is 100.
10 1002 =
log 100 = 210
0335
-
0336
-
Performance #2
Chapter 1 Lesson 2
Basic Logarithms
Name 3 parts to logarithms and how to say them.
0337
-
log 1 ,000 = x10
What exponent goes with each logarithm?
log 1 ,000,000 = x10
0338
-
log 1,000 = 310
log 1,000,000 = 610
1,000 is 3 and 1,000,000 is 6.
0339
-
log 100 = x10
What exponent goes with each logarithm?
log 1 = x10
0340
-
100 is 2 and 1 is 0.
log 100 = 210
log 1 = 010
0341
-
Find the real numbers.
log x = 3
log x = 2
0342
-
log 1,000 = 3
log 100 = 2
3 is 1000 thousand and 2 is 100.
0343
-
Find the real numbers.
log x = 7
log x = 9
0344
-
7 is 10 million and 0 is 1 billion.
log 10,000,000 = 7
log 1,000,000,000 = 9
0345
-
log 1 ,000 = 310
Change this log to exponent form.
0346
-
10 10003 =
log 1000 = 310
10 to the 3rd is 1000.
0347
-
Change this log to exponent form.
log 10 = 110
0348
-
10 to the first is 10.
10 101 =
log 10 = 110
0349
-
0350
-
1. Change Exponents to Logs..3512.3. Questions 1..........................3944. Questions 2..........................4135. Performance 1.....................4326. Performance 2.....................446
Chapter 1 Lesson 3Basic Logarithms
0351
-
Chapter 1 Lesson 3
Basic Logarithms
Change Exponent form to Logarithm form
0352
-
I keep on thinking about going camping.
0353
-
Camping? Because you use logs to make a fire?
0354
-
I'm glad you thought of it.Think of it, real logs this time.
0355
-
Oh, yeah. It would probablyrain and we'd sit by a lighter.
0356
-
Well, think about it.I'm an expert at real logs.
0357
-
I'm an expert at calling forpizza. Well, more stuff to do.
0358
-
log 100 = 210
What did we use to get exponent form?
0359
-
log 100 = 210
The number 7. I'll show you.
0360
-
log 100 = 210
Base to exponent across to real number.
0361
-
log 100 = 210
I'm impressed. Time for the next step.
0362
-
10 = 1,0003
So, what are we doing now?
0363
-
10 = 1,0003
You know how to go from logto exponent. We'll go backwards.
0364
-
Total, 100%, turbo brain power.
How do you change an exponent to logarithm form?
0365
-
10 = 1,0003
This figure is kind of like the 7. You can follow it to make a log.
0366
-
10 = 1,0003
What does it make, a pretzel?
0367
-
10 = 1,0003
It's an .
(That's a 7 turned upside down.)
L
0368
-
10 = 1,0003
Where does it start?It can't start at the base number.
0369
-
10 = 1,0003
Nope, it starts at the other end.
0370
-
10 = 1,0003
Say logarithm of 1000.
Watch where it goes.
Use the Real Number.
0371
-
10 = 1,0003
Logarithm of 1000, Base 10 .
Last step?
Next, go across.
0372
-
10 = 1,0003
Finish the L.Log of 1000, base 10, is 3.
log 1 ,000 = 310
0373
-
10 10,0004
Where does it start?
Change this exponent to log form.
=
0374
-
10 10,0004 =
Start at logarithm of 10,000.
log 10,000
0375
-
10 10,0004 =
Then across to base 10. Here it is...
log 10,00010
0376
-
10 10,0004 =
log 10,000 = 410
Log of 10,000, base 10 is 4.
0377
-
10 = 100,0005
Change this exponent to log form.
All in 1 step.
0378
-
log 100,000 = 510
Start at Log of 100,000, then base 10 is 5.
10 = 100,0005
0379
-
2 = 8x
We'll do more of this later, but what would this exponent be?
0380
-
2 = 8x
I know 2 x 2 x 2 is 8.
0381
-
2 = 83
Right, 2 cubed is 8.So, what's the log form?
0382
-
2 = 83
Ok, start at 8 and go across.
0383
-
2 83 =
log 8 = 32
That's log of 8, base 2, is 3.
0384
-
That's the idea. Any questions?
0385
-
Logs
You know, anytime you want to work with real logs, let me know.
0386
-
Next time I see your dad I'll tellhim to let you cut some wood up.
0387
-
Qs
Where do you start to change log into exponent form?
10 = 1002
0388
-
Start w ith the real number.
10 = 1002
What shape shows the logarithm?
0389
-
10 = 1002
Real number to the base, then up to the exponent.
Use the L.
0390
-
4 = 16?
Change to a log.What's this exponent?
0391
-
4 162 =
log 16 = 24
Log of 16, base 2, is 4.
0392
-
0393
-
Practice #1
Chapter 1 Lesson 3
Basic Logarithms
Change Exponent form to Logarithm form
0394
-
Where do you start to change a log into exponent form?
10 = 1002
0395
-
Start w ith the real number.
10 = 1002
What shape shows the logarithm?
0396
-
10 = 1002
Real number to the base, then up to the exponent.
Use the L.
0397
-
4 = 16?
Change to a log.What's this exponent?
0398
-
4 162 =
log 16 = 24
Log of 16, base 2, is 4.
0399
-
10 = 1002
Where do you start to get alog from an exponent equation?
Problems
0400
-
10 = 1002
Where does it go from there?
Start at the real number. log 100
0401
-
10 = 1002
What is the last step?
Across tothe base. log 10010
0402
-
10 = 1002
It follows an L shape.
Upto theexponent. log 100 = 210
0403
-
Find the exponent, then find the logarithm form.
10 = 10,000x
0404
-
10 = 10,0004
log 10,000 = 410log of 10,000, base 10, is 4.
0405
-
Find the exponent, then find the logarithm form.
10 = 1,000,000x
0406
-
10 = 1,000,0006
log 1 ,000,000 = 610log of 1,000,000, base 10, is 6.
0407
-
What's the log form for 27, base 3?
3 = 27x
0408
-
3 = 273
log 27 = 33log of 27, base 3, is 3.
0409
-
What's the log form for 16, base 2?
2 = 16x
0410
-
2 = 164
log 16 = 42log of 16, base 2, is 4.
0411
-
0412
-
Practice #2
Chapter 1 Lesson 3
Basic Logarithms
Change Exponent form to Logarithm form
0413
-
Where do you start to change log into exponent form?
10 = 1002
0414
-
Start w ith the real number.
10 = 1002
What shape shows the logarithm?
0415
-
10 = 1002
Real number to the base, then up to the exponent.
Use the L.
0416
-
4 = 16?
Change to a log.What's this exponent?
0417
-
4 162 =
log 16 = 24
Log of 16, base 2, is 4.
0418
-
10 = 10003
Where do you start to get alog from an exponent equation?
Problems
0419
-
10 = 10003
Where does it go from there?
Start at the real number. log 1000
0420
-
10 = 10003
What is the last step?
Across tothe base. log 100010
0421
-
10 = 10003
It follows an L shape.
Upto theexponent. log 1000 = 310
0422
-
Find the exponent, then find the logarithm form.
10 = 100,000x
0423
-
10 = 100,0005
log 100,000 = 510log of 100,000, base 10, is 5.
0424
-
Find the exponent, then find the logarithm form.
10 = 10,000,000x
0425
-
10 = 10,000,0007
log 10,000,000 = 710log of 10,000,000, base 10, is 7.
0426
-
What's the log form for 125, base 5?
5 = 125x
0427
-
5 = 1253
log 125 = 35
log of 125, base 5, is 3.
0428
-
What's the log form for 64, base 2?
2 = 64x
0429
-
2 = 646
log 64 = 62log of 64, base 2, is 6.
0430
-
0431
-
Performance #1
Chapter 1 Lesson 3
Basic Logarithms
Change Exponent form to Logarithm form
0432
-
Change this exponent to logarithm form.
10 = 1,0003
0433
-
log 1000 = 310
Log of 1000, base 10 is 3.
10 = 1,0003
0434
-
What's the logarithm form?
10 = 1002
0435
-
log 100 = 210
Log of 100, base 10 is 2.
10 = 1002
0436
-
Solve it and change to log form.
10 = x6
0437
-
log 1 ,000,000 = 610
Log of 1 million, base 10 is 6.
0438
-
Solve it and change to log form.
10 = x8
0439
-
log 100,000,000 = 8
Log of 100 million, base 10 is 8.
0440
-
What's the log form for 64, base 4?
4 = 64x
0441
-
4 = 643
log 64 = 34log of 64, base 4, is 3.
0442
-
What's the log form for 625, base 5?
5 = 625x
0443
-
5 = 6254
log 625 = 45
log of 625, base 5, is 4.
0444
-
0445
-
Performance #2
Chapter 1 Lesson 3
Basic Logarithms
Change Exponent form to Logarithm form
0446
-
Change this exponent to logarithm form.
10 = 10,0004
0447
-
log 10,000 = 410
Log of 10,000, base 10 is 4.
10 = 10,0004
0448
-
What's the logarithm form?
10 = 101
0449
-
log 10 = 110
Log of 10, base 10 is 1.
10 = 101
0450
-
Solve it and change to log form.
10 = x5
0451
-
log 100,000 = 510
Log of 100,000 base 10 is 5.
0452
-
Solve it and change to log form.
10 = x7
0453
-
log 10,000,000 = 7
Log of 10 million, base 10 is 7.
0454
-
What's the log form for 64, base 2?
2 = 64x
0455
-
2 = 646
log 64 = 62log of 64, base 2, is 6.
0456
-
What's the log form for 81, base 3?
3 = 81x
0457
-
3 = 814
log 81 = 43
log of 81, base 3, is 4.
0458
-
0459
-
1. Find the log for 2 and 4.......4602. Find the log for 3 and 6.......5213. Questions 1.........................5664. Questions 2.........................5865. Performance 1.....................6066. Performance 2.....................620
Chapter 1 Lesson 4Basic Logarithms
0460
-
Chapter 1 Lesson 4
Basic Logarithms
Find the log exponent for numbers beginning with 2 and 4.
0461
-
I hate to say it. I'm sickof numbers that begin with 1.
0462
-
I have the cure. 2s
You will love doing this part.
0463
-
2s
2s? That's it?I thought we'd do 2 through 9.
0464
-
We will, but you have to understand how exponents make numbers.
Here's the 1st problem.
0465
-
You know the place value part of this number.
log 20
0466
-
Sure, 20 has 1 place after the 1st digit.
log 20
0467
-
1 . ?place value decimal part
There's the place value part for 20. That's 1 place.
Guess what's next?
0468
-
What's the rest of it?
Decimal for 2?
0469
-
1 . ?place value decimal part
Decimal PartThat's where you find the log exponent for 2. Watch.
0470
-
1 . 30place value decimal part
Decimal PartThe log exponent is 1.30. Any questions?
0471
-
Lost. Already. Not alittle lost. 100% lost.
0472
-
I knew that. Let's go back to exponent form.
0473
-
You know that 10 to the 1st power equals 10.
10 = 101
0474
-
Yeah, it has 1 zero.
10 = 101
0475
-
10 = 2?
What happens whenwe find the exponent for 2?
0476
-
10 = 2?
Well, it's less than 1.
0477
-
Right. It's the decimal 0.30.
10 20.30
We could write 0.3010 , but 100ths are easier to work with.
=
0478
-
10 20.30
=
OK, I see that, but how does that work with logarithms?
0479
-
log 2 = 0.30
The log exponent for 2 is 0.30.
≅
0480
-
log 2 = 0.30
What does the squiggly line mean?
≅
0481
-
log 2 = 0.30
It's not an exact answer. We rounded it.
≅
0482
-
log 2 = 0.30
Ok, show me another one.
≅
0483
-
log 20 = ?.30
If it's the log of 20, how does the log exponent change?
≅
0484
-
log 20 = ?.30
It changes the place value part.
≅
0485
-
log 20 = 1.30
Right. Now it's log 20, base 10, 1.30.
≅
0486
-
log 20 = 1.30
Make an even bigger one.
≅
0487
-
log 2000 = ?
So, what's the exponent for 2000?
0488
-
log 2000 = ?
3 places and the exponent for 2 is 0.30. I think I got this.
0489
-
log 2000 = 3.30
Right. Place value and decimal.
I do have a memory trick you can use for this.
3 places
≅
0490
-
log 2 = 0.30
See log of 2, remember the 3.
≅
0491
-
Ok. What's the next number?
log 2 = 0.30≅
Oh, because it's 2 then 3.
0492
-
log 4 = ? realnumber
logarithm exponent
You can use log of 2 to find 4.
≅
0493
-
log 4 = ? realnumber
logarithm exponent
How are you going to do that?
≅
0494
-
log 4 = ? realnumber
logarithm exponent
≅
What 's 2 + 2?
0495
-
log 4 = ? realnumber
logarithm exponent
≅
4, why does that matter?
4
0496
-
log 4 = 0.60
Another memory trick.0.30 + 0.30 equals log 4.
Ok, what's the log of 4?
≅
0497
-
log 4 = 0.60≅
Sweet! Just double 0.30.
0 .30 + 0.30 = 0.60What's the problem?
0498
-
4,000
What's the 1st step to find a log exponent?
0499
-
3. ?3 Places in 4,000
Find place value. It's 3 places.
Ok, the decimal for 4 is next.
0500
-
3. ?3 Places in 4,000
You're right. What's the decimal for 4?
0501
-
3.603 Placesin 4,000
The first digit, 4.
Double 0.30 is 0.60.
0502
-
3.603 Placesin 4,000
The first digit, 4.
I'll put it altogether.
0503
-
log 4000 = 3.60 realnumber
logarithm exponent
Here's logarithm form.
Tell me the exponent form.
≅
0504
-
10 = 4 ,0003.6
10 to the 3.6 power is 4000. Are we done yet?
≅
0505
-
Just one more log problem. What should it be?
0506
-
log 400
What's the log exponent for 400?
0507
-
log 400 = 2.60
That's weird how 2 + 2 works with log exponents.
≅
Log of 400, base 10, is 2.60.
0508
-
It makes sense in an exponent way.
0509
-
So, when are we doingall the other numbers?
0510
-
We did 2 and 4. The next 2 numbers follow the same pattern.
Don't worry. We'll find all of them.
0511
-
Qs
log 2000 = 3.30
Name 2 parts to a log exponent.
≅
0512
-
log 2000 = 3.30
1. Place Value Part2. Decimal for 1st digit .
2 parts to a log exponent
≅
0513
-
log 2 = 0.30
How can you remember log of 2?
0514
-
log 2 = 0.30
See 2, think 3.
0515
-
log 4 = ?
What's the log exponent for 4?
0516
-
log 4 = 0.60
Log of 4, base 10, is 0.60
0517
-
log 4 = 0.60
How can you remember log of 4?
0518
-
2 + 20.30 + 0.30
Double 2 to find 4.
log 4 = 0.60
0519
-
0520
-
Chapter 1 Lesson 4
Basic Logarithms
What are the log exponents of 3 and 6?
0521
-
Okay, dokey. I've got logs of 2 and 4 down. What's the next log?
0522
-
We'll find the log of 3.You have to remember it.
0523
-
realnumber
log exponent
Log of 3 is 0 .48Remember this exponent.
log 3 = 0.48≅
0524
-
realnumber
log exponent
Got a memory trick for it?
log 3 = 0.48≅
0525
-
log 3 = 0.48 realnumber
log exponent
See 3, then think 4 and double 4 is 8.
Sure, think about this.
Time for a problem.
0526
-
log 300
What's the log exponent for 300?
0527
-
log 300
I'm guessing it starts with the place part.
0528
-
2 . ?
log 300
2 Places
It's the log of 100, 2. What's the exponent for 3?
0529
-
2 . 482 Places The first
digit is 3
See 3, think 48.Ok, I get it now.
0530
-
2 . 482 Places The first
digit is 3
Same deal as the other logs.
0531
-
log 300 = 2.48
2 places and log of 3 is 0.48.
≅
Log of 300 is 2.48.
0532
-
This can be habit forming. I'll make a bigger one.
0533
-
log 3,000,000
Find the log exponent for 3,000,000.
0534
-
log 3,000,000
This is almost like too easy.
0535
-
6 . 48
log 3,000,000 = 6.48
6 Places The first digit is 3
6 places and 0.48 for 3.
≅
0536
-
log 3 = 0.48
Can you use log of 3 to find other logs like 2 did?
≅
0537
-
log 3 = 0.48
Abracadabra, log of 6. I'll start off with a trick.
≅
0538
-
Add 0.30
log 3 = 0.48+ 0.30
Exactly the same as finding log 4. So, what's the log of 6?
0539
-
log 6 = 0.78
This one is easy to remember.
Add 0.48 to 0.30. It's 0.78
0540
-
log 6 = 0.78
How do you remember it?
0541
-
log 6 = 0.78
See log 6 and think 78 are next.
≅
0542
-
log 6 = 0.78
Sure. Or you can add 0.30. I'll get another problem.
≅
0543
-
log 6000
What's the log exponent?
0544
-
log 6000
Start with the place value part.
That's a 3 for 1000.
0545
-
3 . ?3 Places The first
digit is 6
log 6000
What's the decimal part?
0546
-
log 6 = 0.78
See the log of 6,then 78 are the decimals.
It's so abc 's. I like that.Like 1,2,3 a,b,c.
≅
0547
-
log 6000 = 3.78
ABC, 123. Michael Jackson would've liked that.
≅
0548
-
log 6000 = 3.78
I'm so into the basics.Are we almost done?
≅
0549
-
log 600,000
Find the log exponent for 600,000.
All 1 step, do the answer.
0550
-
Start w ith 0.48
Add 0.30
Here's the way you find it. Add 0.30, just like log 4.
0551
-
Start w ith 0.48
Add 0.30
Finish this log equation off.
0552
-
log 600,000 = 5.78
I think 2 is my favorite one.
≅
0553
-
You can count your toes if that works.
0554
-
5 7 8 9
So, where's 5, 7, 8, and 9?
0555
-
Practice 2, 3, 4, and 6.We'll do those tomorrow.
0556
-
Qs
log 3 = 0.48
What's the log exponent for 3?
≅
0557
-
log 3 = 0.48≅
log of 3 is 48 100ths.
0558
-
log 3 = 0.48≅
How can you remember log 3?
0559
-
log 3 = 0.48
3 4 8Remember log 3, think...
then and
≅
0560
-
log 6 = ?≅
What's the log exponent for 6?
0561
-
log 6 = 0.78≅
log of 6 is 78 100ths.
0562
-
log 6 = 0.78≅
How can you remember it?
0563
-
log 6 = 0.78
6 78
0.48 + 0.30
You can count 6, 7, 8.
then
≅
Or Add log of 2, 0.30.
0564
-
0565
-
Practice #1
Chapter 1 Lesson 4
Basic Logarithms
Find the log exponent for numbers with 2, 4, 3 and 6.
0566
-
log 2000 = 3.30
Name 2 parts to a log exponent.
≅
0567
-
log 2000 = 3.30
1. Place Value Part2. Decimal for 1st digit .
2 parts to a log exponent
≅
0568
-
log 2 = 0.30
How can you remember log of 2?
0569
-
log 2 = 0.30
See 2, think 3.
0570
-
log 4 = ?
What's the log exponent for 4?
0571
-
log 4 = 0.60
Log of 4, base 10, is 0.60
0572
-
log 4 = 0.60
How can you remember log of 4?
0573
-
2 + 20.30 + 0.30
Double 2 to find 4.
log 4 = 0.60
0574
-
Problems
log 2,000,000
What's the 1st step to find a log exponent?
0575
-
Log 2,000,000
Find the place value part . What's the 2nd step?
6.
0576
-
Log 2,000,000
6.30
Log of 2,000,000, base 10, is 6.30.
Decimal exponent for 2 .
0577
-
What's the 1st step for log of 40,000?
log 40,000
0578
-
Log 40,000
Find the place value part . What's the 2nd part?
4.
0579
-
Log 40,000
Log of 40,000, base 10, is 4.60.
4.60
0580
-
log 2,000
All in 1 step.What's the log exponent?
0581
-
Log 2,000
Log of 2,000, base 10, is 3.30.
3.30
0582
-
log 40,000
All in 1 step.What's the log exponent?
0583
-
Log of 40,000, base 10, is 4.60.
4.60
log 40,000
0584
-
0585
-
Practice #2
Chapter 1 Lesson 4
Basic Logarithms
Find the log exponent for numbers with 2, 4, 3 and 6.
0586
-
log 3 = 0.48
What's the log exponent for 3?
≅
0587
-
log 3 = 0.48≅
log of 3 is 48 100ths.
0588
-
log 3 = 0.48≅
How can you remember log 3?
0589
-
log 3 = 0.48
3 4 8Remember log 3, think...
then and
≅
0590
-
log 6 = ?≅
What's the log exponent for 6?
0591
-
log 6 = 0.78≅
log of 6 is 78 100ths.
0592
-
log 6 = 0.78≅
How can you remember it?
0593
-
log 6 = 0.78
6 78
0.48 + 0.30
You can count 6, 7, 8.
then
≅
Or Add log of 2, 0.30.
0594
-
Problems
log 300,000
Find the log exponent.
5.30 5.48 5.60 5.78
0595
-
Log 300,000, base 10, is 5.48.
Log 300,000
5.48
0596
-
Find the log exponent.
3.30 3.48 3.60 3.78
log 6000
0597
-
Log 6,000, base 10, is 3.78.
Log 6000
3.78
0598
-
Find the log exponent.
7.30 7.48 7.60 7.78
log 30,000,000
0599
-
Log 30,000,000, base 10, is 7.48.
Log 30,000,000
7.48
0600
-
log 600
Find the log exponent.How do you remember 6?
0601
-
See 6, remember 78.Log 600, base 10, is 2.78.
Log 600
2.78
0602
-
log 3,000
Find the log exponent.
0603
-
Log 3000, base 10, is 3.48.
Log 3,000
3.48
0604
-
0605
-
Performance #1
Chapter 1 Lesson 4
Basic Logarithms
Find the log exponent for numbers with 2, 4, 3 and 6.
0606
-
log 200 = x
log 400 = x
Find the log exponents.
0607
-
log 200 = 2 .30
log 400 = 2 .60
0608
-
log 3000 = x
log 60,000 = xFind the log exponents.
0609
-
log 3000 = 3 .48
log 60,000 = 4 .78
0610
-
log 20 = x
log 30 = x
Find the log exponents.
0611
-
log 20 = 1 .30
log 30 = 1 .48
0612
-
x10 = 40,000
10 = 20,000Find the exponents.
x
0613
-
10 = 40,000
10 = 20,000
4.60
4.30
0614
-
Find the exponents.
x10 = 300
10 = 600x
0615
-
10 = 300
10 = 600
2.48
2.78
0616
-
10 = x
10 = x
2.30
2.60
0617
-
10 = 2000
10 = 4000
2.48
2.78
0618
-
0619
-
Performance #2
Chapter 1 Lesson 4
Basic Logarithms
Find the log exponent for numbers with 2, 4, 3 and 6.
0620
-
log 20 = x
log 4,000 = x
Find the log exponents.
0621
-
log 20 = 1 .30
log 4000 = 3 .60
0622
-
log 30 = x
log 6,000 = xFind the log exponents.
0623
-
log 30 = 1 .48
log 6000 = 3 .78
0624
-
log 200 = x
log 300 = x
Find the log exponents.
0625
-
log 200 = 2 .30
log 300 = 2 .48
0626
-
x10 = 4000
10 = 2000Find the exponents.
x
0627
-
10 = 4000
10 = 2000
3.60
3.30
0628
-
Find the exponents.
x10 = 3000
10 = 6000x
0629
-
10 = 3000
10 = 6000
3.48
3.78
0630
-
10 = x
10 = x
3.48
3.78
0631
-
10 = 3000
10 = 6000
3.48
3.78
0632
-
0633
-
1. The log for 7, 8, and 9?......6342. The log exponent of 5.........6853. Questions 1........................7104. Questions 2........................7335. Performance 1....................7506. Performance 2....................764
Chapter 1 Lesson 5Basic Logarithms
0634
-
Chapter 1 Lesson 5
Basic Logarithms
What are the log exponents for 7, 8, and 9?
0635
-
I never thought it wouldtake so long to count to 9.
0636
-
Well, 3 and 6 went together just like 2 and 4 did.
But, the rest are different.
0637
-
So, do you add 0.30 or what?
0638
-
You add, but 7, 8, and 9 add a different number.
I'll start off with log exponent for 8.
0639
-
I know how to remember this.
log 8 = 0.90≅
0640
-
log 8 = 0.90
With your brain.How about that 8 with a 9?
≅
0641
-
See 8, think 9.
log 8 = 0.90≅
That totally works.
0642
-
log 8 = 0.90
We'll do the log of 7 next.Another ABC, 1, 2, 3.
≅
0643
-
Ok, this is going to surprise you.
log 7 = log 8 = 0.90 ≅
≅
0644
-
7 takes 5 100ths away.
log 7 = 0.85log 8 = 0.90
How are you going to remember it?
≅
≅
0645
-
log 7 = 0.85≅
Kind of like 3 had 48.
7, remember 8 and 5.
0646
-
log 7 = 0.85≅
Log of 9 does the same thing.
What is that?
0647
-
9 adds 5 100ths.
log 8 = 0.90log 9 = 0.95
This one is easy to remember.
≅
≅
0648
-
9 is the only one that has the same digit next.
log 9 = 0.95≅
0649
-
log 7 = 0.85log 8 = 0.90log 9 = 0.95
≅
≅
≅
Add 0.05.
Add 0.05.
I told you it was different.
0650
-
log 7 = 0.85log 8 = 0.90log 9 = 0.95
≅
≅
≅
Add 0.05.
Add 0.05.
Yeah, go over them again.
0651
-
log 8 = 0.90
Think about it my way.
How do you find the log of 7?
≅
0652
-
log 7 = 0.85log 8 = 0.90≅
≅
Take 5 100ths away. That's 0.05.
0653
-
log 7 = 0.85log 8 = 0.90≅
≅
Okay, Log of 9 is the easy one.
0654
-
log 8 = 0.90log 9 = 0.95
≅
≅
Add 5 100ths to log of 8.
0655
-
log 8 = 0.90log 9 = 0.95
≅
≅
How can you remember it?
0656
-
log 9 = 0.95≅
Only 9 has the same number as it's exponent.
0657
-
log 9 = 0.95≅
Now I'll do a few logs with it.
0658
-
log 7,000
Find the log exponent for 7,000.
0659
-
log 7,000
I've got to remember this.
0660
-
3 . 853 Places The first
digit is 7and
log 7,000 = 3.85≅
85 takes 5 100ths away from 0.90.
0661
-
Nice, now one with an 8.
0662
-
log 800
Find the log exponent for 800.
0663
-
log 800
Puts the easy in the cheezy.
0664
-
2 . 90
log 800 = 2.90
2 Places The first digit is 8
and
≅
8, then 9. 8's my favorite.
0665
-
Last one with you know what.
0666
-
log 90,000,000
Oooh, big number.
0667
-
log 90,000,000
Find the log exponent for 90,000,000.
0668
-
7 . 95
log 90,000,000 = 7.95
7 Places The first digit is 9
and
≅
That went faster than 2s and 4s
0669
-
I kind of like the 5 100ths part.
0670
-
Log exponents is one of the most unusual things we've done in math.
You have to admit.
0671
-
I used to think subtraction was tough.
0672
-
Qs
What's the log exponent for 7?
log 7 = ?≅
0673
-
log 7 = 0.85≅
Log of 7 is 85 100ths.How can you remember it?
0674
-
log 7 = 0.85≅
Remember...7 think 85
0675
-
What's the log exponent for 8?
log 8 = ?≅
0676
-
log 8 = 0.90≅
Log of 8 is 9 10ths.How do you remember it?
0677
-
8 90thenSee 8, remember 9.
log 8 = 0.90≅
0678
-
What's the log exponent for 9?
log 9 = ?≅
0679
-
log 9 = 0.95≅
Log of 9 is 95 100ths.Why is it different?
0680
-
log 9 = 0.95
It's the only one with double digits. 9 follows 9.
≅
0681
-
log 7 = 0.85log 8 = 0.90log 9 = 0.95
Start at log 7. How do you get 8 and 9?
0682
-
log 7 = 0.85log 8 = 0.90log 9 = 0.95
Add 0.05 to each
Add 0.05
Add 0.05
0683
-
0684
-
Chapter 1 Lesson 5a
Basic Logarithms
What is the log exponent of 5?
0685
-
I think we've got all of the log exponents.
0686
-
Who taught you to count?
0687
-
Actually, that was you.
0688
-
Well, I did a terrible job.Log of 5 is one you remember.
Here it is....
0689
-
log 5 = 0.70
They're both odd numbers.
≅
It equals 70 100ths.
0690
-
log 5 = 0.70
Actually, there is a way to use log of 4 to remember it.
≅
0691
-
log 4 = 0.60
Remember 4, 5makes exponent 6, 7.
log 5 = 0.70≅
≅
0692
-
log 4 = ?
It also works if you can't remember log of 4.
log 5 = 0.70≅≅
0693
-
log 4 = ?log 5 = 0.70≅
≅
It's alittle late for that.
0694
-
log 4 = 0.60log 5 = ?
≅
≅
Okay, what's the log of 5?
0695
-
log 5 = 0.70≅
Duh, we just did this. Log of 5 is 0.70.
0696
-
log 5 = 0.70≅
Just checking. I'll make a problem.
0697
-
What is the log exponent?
log 50,000
0698
-
Log 50,000 = 4.70
Logarithm of 50,000, base 10, is 4 .70.
I thought Log of 5 would be 0.5.
≅
0699
-
log 5 = 0.70
All logs are alittle higher.
Think of it's exponent form.
≅
0700
-
10 = 50.7log 5 = 0.70
Like all the others, the logarithm shows the exponent.
0701
-
Decimal Log Exponents
Finally, all the log exponents done. It took like a year.
0702
-
You'll like the next part.We get to go backwards.
0703
-
Qs
log 5 = ?What's the log exponent of 5?
≅
0704
-
How can you remember log 5?
log 5 = 0.70
The log of 5 is 0 .7 10ths.
≅
0705
-
log 5 = 0.70≅
They're both odd numbers.
0706
-
log 4 = ?log 5 = ?
≅
≅
How can you use log 4 to remember 5?
0707
-
log 4 = 0.60log 5 = 0.70
≅
≅
It goes 4, 5, then 6, 7.
0708
-
0709
-
Practice #1
Chapter 1 Lesson 5
Basic Logarithms
What are the log exponents for 5, 7, 8, and 9?
0710
-
What's the log exponent for 7?
log 7 = ?≅
0711
-
log 7 = 0.85≅
Log of 7 is 85 100ths.How can you remember it?
0712
-
log 7 = 0.85≅
Remember...7 think 85
0713
-
What's the log exponent for 8?
log 8 = ?≅
0714
-
log 8 = 0.90≅
Log of 8 is 9 10ths.How do you remember it?
0715
-
8 90thenSee 8, remember 9.
log 8 = 0.90≅
0716
-
What's the log exponent for 9?
log 9 = ?≅
0717
-
log 9 = 0.95≅
Log of 9 is 95 100ths.Why is it different?
0718
-
log 9 = 0.95
It's the only one with double digits. 9 follows 9.
≅
0719
-
log 7 = 0.85log 8 = 0.90log 9 = 0.95
Start at log 7. How do you get 8 and 9?
0720
-
log 7 = 0.85log 8 = 0.90log 9 = 0.95
Add 0.05 to each
Add 0.05
Add 0.05
0721
-
Find the log exponent.
6.70 6.85 6.90 6.95
Problems
log 7,000,000
0722
-
Log of 7,000,000, base 10, is 6.85.
Log 7,000,000
See 7, think 85.
6.85
0723
-
Find the log exponent.
4.70 4.85 4.90 4.95
log 50,000
0724
-
Log 50,000
Both 5 and 7 are odd.
4.70
Log of 50,000, base 10, is 4.70.
0725
-
log 800
Find the log exponent.How do you remember 8?
0726
-
2.90
Log 800
Log of 800, base 10, is 2.90.
See 8, 9 is after it .
0727
-
Find the log exponent. Why is 9 different?
log 90,000
0728
-
4.95
Log 90,000
Log of 90,000, base 10, is 4.95.
Only 9 starts the same, 95.
0729
-
log 500,000
Find the log exponent.How can you remember 5?
0730
-
5.70
Log 500,000
Log of 500,000, base 10, is 5.70.
5 and 7, they're both odd.
0731
-
0732
-
Practice #2
Chapter 1 Lesson 5
Basic Logarithms
What are the log exponents for 5, 7, 8, and 9?
This lesson is different from the first.
0733
-
log 5 = ?What's the log exponent of 5?
≅
0734
-
How can you remember log 5?
log 5 = 0.70
The log of 5 is 0 .7 10ths.
≅
0735
-
log 5 = 0.70≅
They're both odd numbers.
0736
-
log 4 = ?log 5 = ?
≅
≅
How can you use log 4 to remember 5?
0737
-
log 4 = 0.60log 5 = 0.70
≅
≅
It goes 4, 5, then 6, 7.
0738
-
Find the log exponent.
5.70 5.85 5.90 5.95
Problems
log 500,000
0739
-
Log of 500,000, base 10, is 5.70.
Log 500,000
5.70
0740
-
Find the log exponent.
3.30 3.48 3.60 3.78
log 4,000
0741
-
Log 4,000
3.60
Log of 4,000, base 10, is 3.60.
0742
-
log 9000
Find the log exponent.
0743
-
3.95
Log 9000
Log of 9000, base 10, is 3.95.
0744
-
Find the log exponent.
log 200,000
0745
-
5.30
Log 200,000
Log of 200,000, base 10, is 5.30.
0746
-
log 3,000,000
Find the log exponent.
0747
-
6.48
Log 3,000,000
Log of 3,000,000, base 10, is 6.48.
0748
-
0749
-
Performance #1
Chapter 1 Lesson 5
Basic Logarithms
What are the log exponents for 5, 7, 8, and 9?
0750
-
log 8000 = x
log 7000 = x
Find the log exponents.
0751
-
log 8000 = 3 .90
log 7000 = 3 .85
0752
-
log 50 = x
log 9,000 = x
Find the log exponents.
0753
-
log 50 = 1 .70
log 9000 = 3 .95
0754
-
log 80,000 = x
log 90,000 = xFind the log exponents.
0755
-
log 80,000 = 4 .90
log 90,000 = 4 .95
0756
-
x10 = 70
10 = 80x
Find the real numbers.
0757
-
1.85
1.90
10 = 70
10 = 80
0758
-
x10 = 500
10 = 900x
Find the real numbers.
0759
-
2.70
2.95
10 = 500
10 = 900
0760
-
x10 = 700
10 = 800x
Find the real numbers.
0761
-
2.8510 = 700
10 = 8002.90
0762
-
0763
-
Performance #2
Chapter 1 Lesson 5
Basic Logarithms
What are the log exponents for 5, 7, 8, and 9?
0764
-
log 80 = x
log 90 = x
Find the log exponents.
0765
-
log 80 = 1 .90
log 90 = 1 .95
0766
-
log 700 = x
log 90,000 = x
Find the log exponents.
0767
-
log 700 = 2 .85
log 90,000 = 4 .95
0768
-
log 50,000 = x
log 70,000 = xFind the log exponents.
0769
-
log 50,000 = 4 .70
log 70,000 = 4 .85
0770
-
x10 = 700
10 = 800x
Find the real numbers.
0771
-
2.8510 = 700
10 = 8002.90
0772
-
x10 = 8000
10 = 9000x
Find the real numbers.
0773
-
3.9010 = 8000
10 = 90003.95
0774
-
x10 = 50,000
10 = 70,000x
Find the real numbers.
0775
-
4.7010 = 50,000
10 = 70,0004.85
0776
-
0777
-
1. Name 2 steps to find a real number..7782.3. Questions 1......................................8184. Questions 2......................................8375. Performance 1.................................8566. Performance 2.................................870
Chapter 1 Lesson 6Basic Logarithms
0778
-
Chapter 1 Lesson 6
Basic Logarithms
Name 2 steps to find the real number for a log exponent.
0779
-
Going Backw ards
How does a log go backwards?
0780
-
You know the log exponent. Find it's real number.
Sounds like a joke.
Here's a problem.
0781
-
log x = 1.60
See, something like this. It finds the real number.
0782
-
log x = 1.60
Do I find the place value or the decimal part first?
0783
-
log x = 1.60
Either is fine, but, since we read numbers left to right, we'll start with the decimal part first.
What does the decimal 0.60 find?
0784
-
log x = 1.60
Easy sneezy. 0.60 is log 4.
4____
0785
-
log x = 1.60
4____So, what does the 1 show you?
0786
-
log 40 = 1.60
1 means there's 1 place, so the real number is 40.
40I t counts place value.
0787
-
log 40 = 1.60
That's how you find thereal number from an exponent.
40
Here's another one...
0788
-
log x = 2.30
Find the real number thatmakes this logarithm (base 10).
What's the first digit?
0789
-
log x = 2.30
2___
The number for 0.30 is 2.
0790
-
log x = 2.30
What's the place value part?
2___
0791
-
log 200 = 2.30
2 places is hundreds.
0792
-
This one was easybecause you learned 2 first.
log 200 = 2.30
0793
-
Another real number, (base 10).
What's the 1st digit?
log x = 3.60
0794
-
The number for 0.60 is 4.
log x = 3.60
4___
0795
-
log x = 3.60
What's the place value part?
4___
0796
-
log 4000 = 3.60
3 places makes thousands.
0797
-
log 4000 = 3.60
log of 4000, base 10, is 3.60
0798
-
Find the real number, all 1 step.
log x = 4.90
0799
-
log 80,000 = 4.90
It's 8 and 4 places is 10,000.
0800
-
log 80,000 = 4.90
Log of 80,000, base 10, is 4.90.
0801
-
Find the real number, all 1 step.
log x = 6.85
That's why I call it going backwards.
0802
-
log 7,000,000 = 6.85
It's 7 and 6 places is millions.
0803
-
log 7,000,000 = 6.85
log of 7 million, base 10, is 6.85.
0804
-
1. Decimal is 1st digit .2 . Place Value
Why do you find the 1st digit first?
0805
-
It's just how we say numbers.The 1st digit always goes first.
0806
-
1. Decimal is 1st digit .2 . Place Value
Oh, that makes sense.
0807
-
Wow. That's the 1st time you said something makes sense in logs.
0808
-
I didn't say that logs make sense. Just how you say a number.
0809
-
Well, at least something makes sense.
0810
-
Qs
log x = 1.60
What's the 1st step to find a real number from an exponent?
0811
-
log x = 1.60
0.60 is log 4.
4____Start w ith the 1st digit .
0812
-
log x = 1.60
What happens after the 1st digit?
4____
0813
-
log 40 = 1.60
Count the place value.
40
1 means it's 40.
0814
-
Name 2 steps to find a real number from a log exponent.
log ? = 1.48
0815
-
1. Find the 1st digit.2. Find the places after it.
log 30 = 1.48Start here.
0816
-
0817
-
Chapter 1 Lesson 6
Basic Logarithms
Practice #1 Name 2 steps to find the real number for a log exponent.
0818
-
log x = 1.60
What's the 1st step to find a real number from an exponent?
0819
-
log x = 1.60
0.60 is log 4.
4____Start w ith the 1st digit .
0820
-
log x = 1.60
What happens after the 1st digit?
4____
0821
-
log 40 = 1.60
Count the place value.
40
1 means it's 40.
0822
-
Name 2 steps to find a real number from a log exponent.
log ? = 1.48
0823
-
1. Find the 1st digit.2. Find the places after it.
log 30 = 1.48Start here.
0824
-
Problems
What's the 1st step to find the real number?
log x = 3.30
0825
-
Log 2____ = 3.30
What's the rest of the number?
The decimal show s 2.
0826
-
Log 2,000 = 3.30
Logarithm of 2,000, base 10, is 3.30.
Find the place value.
0827
-
log x = 1.48
All in 1 step, find the real number.
0828
-
Log 30 = 1.48
Logarithm of 30, base 10, is 1.48.
0829
-
log x = 3.78
Find the real number.
0830
-
Log 6,000 = 3.78
Logarithm of 6,000, base 10, is 3.78.
0831
-
log x = 7.60
Find the real number.
0832
-
Log 40,000,000 = 7.60
Logarithm of 40,000,000 base 10, is 7.60.
0833
-
log x = 2.48
Find the real number.
0834
-
Log 300 = 2.48
Logarithm of 300, base 10, is 2.48.
0835
-
0836
-
Chapter 1 Lesson 6
Basic Logarithms
Practice #2 Name 2 steps to find the real number for a log exponent.
0837
-
Qs
log x = 1.60
What's the 1st step to find a real number from an exponent?
0838
-
log x = 1.60
0.60 is log 4.
4____Start w ith the 1st digit .
0839
-
log x = 1.60
What happens after the 1st digit?
4____
0840
-
log 40 = 1.60
Count the place value.
40
1 means it's 40.
0841
-
Name 2 steps to find a real number from a log exponent.
log ? = 1.48
0842
-
1. Find the 1st digit.2. Find the places after it.
log 30 = 1.48Start here.
0843
-
Problems
What's the 1st step to find the real number?
log x = 4.85
0844
-
Log 7____ = 4.85
What's the rest of the number?
The decimal show s 7.
0845
-
Log 70,000 = 4.85
Logarithm of 70,000, base 10, is 4.85.
Find the place value.
0846
-
log x = 2.85
All in 1 step, find the real number.
0847
-
Log 700 = 2.85
Logarithm of 700, base 10, is 2.85.
0848
-
log x = 5.95
Find the real number.
0849
-
Log 900,000 = 5.95
Logarithm of 900,000, base 10, is 5.95.
0850
-
log x = 4.70
Find the real number.
0851
-
Log 50,000 = 4.70
Logarithm of 50,000 base 10, is 4.70.
0852
-
log x = 3.60
Find the real number.
0853
-
Log 4,000 =