Post on 16-Mar-2016
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10.2 Logarithms and Logarithmic functions
Graphs of a Logarithmic function verse Exponential functions
In RED y = 10x
Graphs of a Logarithmic function verse Exponential functions
In RED y = 10x , In Blue y = Log x
The functions relate in which way?
The Main Concept of Logarithms
Remember the way an exponential function and a Logarithm function is related.
92931,0
32 Log
bbxLOGyxb b
y
The Main Concept
Remember
1,0
bbxLOGyxb b
y
Write in Exponential form
Log 4 16 = 2
21001
10 Log
Write in Exponential form
Log 4 16 = 2
21001
10 Log
1642
100110 2
Write in Logarithmic form
53 = 125
327 31
Write in Logarithmic form
53 = 125
327 31
3125log5
313log27
How to use the Concept to Solve problems
Evaluate
243log3
How to use the Concept to Solve problems
Evaluate
5
332433
243log
243log
5
3
3
x
x
x
x
How to use the Concept to Solve problems
Evaluate 99Log
How to use the Concept to Solve problems
Evaluate
1
99
9
9
1
9
9
x
xLog
Log
x
How to use the Concept to Solve problems
Evaluate kx 1log 277
How to use the Concept to Solve problems
Evaluate
1
1loglog
7
2
277
1log 27
xk
xk
kx
Use the concept
Solve 34log8 n
Use the concept
Solve
16
8
34log
34
8
n
n
n
Use the concept
Solve 3log6 x
Use the concept
Solve
02166
3log
3
6
xx
x
Why Greater then Zero?
Solve for x
Check your solutions
34loglog 42
4 xx
Solve for x
Check your solutions
3,1
031034
34
34loglog
2
2
42
4
x
xxxx
xx
xx
Solve for x
Check your solutions
3,1
031034
34
34loglog
2
2
42
4
x
xxxx
xx
xx
9log9log
334log3log
1log1log314log1log
44
42
4
44
42
4
They both work. What would make the answers not work?
This Logarithm is impossible
Why?
)27(3 Log
This Logarithm is impossible
Try to solve
,273
273
x
xLog
Is there any x that would make it equal -27?
How do you solve
Evaluate the expression
125log5
How do you solve
Evaluate the expression
351255
125log
125log
3
5
5
x
x
x
Homework
Page 536# 21 – 39 odd,
47 – 59 odd
Homework
Page 536# 22 – 40 odd,
48 – 58 odd