Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
e ≈ 2.71828...
Exponential functions with a base of e are useful for
describing continuous growth or decay
x y
­2
e­2 ≈ 0.13534
­1
0
1
2
e­1 ≈ 0.36788
e0 = 1
e1 ≈ 2.78183
e2 ≈ 7.38906
Continuously Compounded Interest
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Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
Continuously Compounded Interest
Section 8.3 Logarithmic Functions as Inverses
Objective:
Be able to write and evaluate logarithmic expressions
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Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
A logarithmic function is the inverse of an
exponential function
exponent
exponent
x
If y = b , then logby = x base
100 = 102
base
log10100 = 2
x
If y = b , then logby = x Common Logarithm - base 10
log10 y = log y
log 1000 = x
x = log 1
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Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
e ≈ 2.71828...
Exponential functions with a base of e are useful for
describing continuous growth or decay
x y
­2
e­2 ≈ 0.13534
­1
0
1
2
e­1 ≈ 0.36788
e0 = 1
e1 ≈ 2.78183
e2 ≈ 7.38906
If y = bx , then logby = x Natural Logarithm - base e
loge y = ln y
ln 25 = x
x = ln 1
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Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
If y = bx , then logby = x
Write in logarithmic form:
729 = 36
100 = 1
7.389 = e2
1 3
2
( ) = 1
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If y = bx , then logby = x
Write in exponential form:
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Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
If y = bx , then logby = x
Evaluate each logarithm:
log4 42
log 10
log4643
log327
If y = bx , then logby = x
GROUP QUIZ
Rewrite each equation in exponential form
Rewrite each equation in logarithmic form
Evaluate each expression
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Lesson 8.3 Logs as Inverses.notebook
March 30, 2012
Homework #20
VIDEO @ www.phschool.com
Use web code age-0803 --> Watch the third video
Problems to do:
Pg 450 #22-25, 35-37 (graphs on graph paper or no credit)
8.1-8.3 QUIZ Next Thurs/Fri
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