Download 10.4 Notes 2013.notebook

10.4 Notes 2013.notebook
Warm Up
x
x
81
1. 34= 3. 3
=9 5. 3
=81 ?
2
x
2. 90= 4. 3
=27 3
1
To find the exact answer for 3x=18 we must use logarithms.
Definition of a logarithm:
Let b & y be positive numbers such that b≠1, then log b y = x
PULL
Common Log
The logarithm with a base of 10 written as
log10 x or just log x.
PULL
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10.4 Notes 2013.notebook
Rewriting Logarithmic Equations
Logarithmic Form
log2 16 = 4
log7 1 = 0
Exponential Form
24=16
70=1
51=5
log5 5 = 1
log 1/100 = -2
10-2=1/100
log1/4 4 = -1
(1/4)-1=4
Rewrite in Exponential Form
log3 81=4
log1/2 4=‐2
log4 4=1
log6 1=0
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10.4 Notes 2013.notebook
Re Write in Log Form:
1.
2.
3.
Re Write in Log Form:
4.
5.
6.
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10.4 Notes 2013.notebook
Special Cases
#1
logb 1 = 0
#2
logb b = 1
#3
logb bx = x
#4
log x
b
b
=x
Evaluating Logarithmic
Expressions
Evaluate log4 64 1st Always set equal to x
2nd Change to exponential form
log4 64 = x
4x=64
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10.4 Notes 2013.notebook
Evaluate:
1. 2.
3.
log2 32
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10.4 Notes 2013.notebook
1. log5 125
2. logx 36 = 2
3.
4.
5x
log10 10
log24
3x
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10.4 Notes 2013.notebook
Solve:
a.)
b.)
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