8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
Today's TargetI Can...
83 Logarithmic Functions as Inverses
...
Alg 2/T
write in log form,exponential form and evaluate logs.
ALG 2 TRIG:
PLEASE LOCATE NOW:
1. WS 82 DAY 1A
2. YESTERDAY'S WS
3. YOUR CALCULATOR
BIG FA TOMORROW!! ON 8.1 & 8.2
THANKS!
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
Please complete before the bell
• logs are exponents
• logs are functions
• logs are inverses of exponential functions
• logby = x is read:
log of y to base b = x or bx = y
8.3 LOGS!!!!I CAN: write in log form, exponential form and evaluate logs.
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
log28 = x
means:
2x = 8
(baseanswer = log)
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
log28 = x
(log part or base part are never negative)
logs are base 10 unless otherwise indicated!
log100 = x
log10100 = x
10x = 100
x = ?
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
log525 = x
5x = 25
x = ? x = 2
Example 1 :
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
log1000 = x
?? = ? 10x = 1000 x = 3
Example 2 :
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log .1 = x
10x = .1
10x = 1/10
10x = 101
x = 1
Example 3 : Example 4 :
logx 36 = 2
think!!
logx 36 = 2
x2 = 36
(x2)1/2 = 361/2
x = 1 361/2
x = 1 6
Example 4 :
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
Can you write the following in log form?
161/2 = 4log164 = 1/2
ex. 5
bx = y• log
by = x
271/3 = 3 log273= 1/3
Can you write the following in
exponential form?
log525 = x
5x = 25
ex 7
WS 8.3
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
Alg 2/trig
Pls take out
1. Your calc
2. Your 8.3 notes and WS
3. YOUR VIP
see me if you missed the FA on Fri
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
ex 8
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ex 9
ex 9
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# 65
Find the concentration of hydrogen ions in maple syrup which has a pH of 5.2.
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Find the inverse of the function.
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WS 8.3
Seismology
The magnitude of an earthquake is a measure of theamount of energy released at its source. TheRichter scale is an exponential measure of earthquake magnitude. An earthquake of magnitude 5releases about 30 times as much energy as anearthquake of magnitude 4.
0 1 2 3 4 5 6 7 8 9
E E(30) E(30)2 E(30)3 E(30)4 E(30)5 E(30)6 E(30)7 E(30)8 E(30)9
Ex. 1 In 1995, an earthquake in Mexico registered 8.0 on the Richter scale. In 2001, an earthquake of magnitude 6.8 shook Washington state. Compare the amounts of energy released in the 2 earthquakes.
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
0 1 2 3 4 5 6 7 8 9
E E(30) E(30)2 E(30)3 E(30)4 E(30)5 E(30)6 E(30)7 E(30)8 E(30)9
E x 308E x 306.8
0 1 2 3 4 5 6 7 8 9
E E(30) E(30)2 E(30)3 E(30)4 E(30)5 E(30)6 E(30)7 E(30)8 E(30)9
• now compare the recent CHILE earthquake (8.8) with the Washington state:
how much more energy was released?
• the RECENT 8.9 in JAPAN???
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To find log 75 you will have to use your calculator use 4 decimal places
log75≈1.8751
Laws of Logs:(regular and natural)
logMN = logM + logN
log M = log M logN N
logMk = klogM
logM = logN M = N
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Simplify according to the laws of logs:
• log4 + log 6 =
• logM + logN2 =
• 2logM - logN =
• 2logM - 3logN =
• ln4 + 2ln3 =
• lnM + 2lnN =
change of base formula:
log430 = log30
log 4
Why you ask?
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log430 = x
4x = 30
log4x = log30
xlog4 = log30
x = log30 log4
The population of a city is:
P = 240,360e.012t
When t = 0, is the year 2000. when will the polulation reach 275,000?
275,000 = 240,360e.012t
ans: the year 2011
8.3 notes USE THIS applications 201516 FINISHED.notebook February 01, 2016
You deposit $500.00 at 6.75% interest
compounded continuously.
How long will it take for it to double?
Remember : A = Pert
1000 = 500e.0675t
2 = e.0675t
ln2 = lne.0675t
ln2 = .0675t
ln2 = t 0675
t = 10.3
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