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7.3 Notes.notebook
January 05, 2017
7.3 Logarithmic Functions as Inverses
Name: ____________________
Objectives: Students will be able to evaluate logarithmic expressions and
graph logarithmic functions.
What in the world is a logarithm?
Logarithms are _____________.
Let b and y be positive numbers with b≠1. The
logarithm of y with base b is denoted logby=x and is defined as follows:
x
logby=x if and only if b =y
In words: logby=x is read "log base b of y".
Common log: log10 x=logx
Natural log: logex=lnx
Feb 14­6:15 PM
Examples: Rewrite in exponential form.
1.) log28=3
2.) log41=0
3.) log12 12=1
4.) log2¼=-2
Examples: Rewrite in logarithmic form.
2
-2
1.) 3 =9
2.) 5 =1/25
-3
0
3.) (½) =8
4.) 4 =1
Examples: Evaluate the logarithms.
1.) log52
2.) log381
3.) log100
4.) ln e
Feb 14­6:26 PM
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7.3 Notes.notebook
5.) log1000
January 05, 2017
6.) log1/3 27
7.) log164
8.) log33
Inverse Functions: The logarithmic function
x
y = logbx and the exponential function y = b are
x
log x
inverses. This means: log bb =x and b b =x.
Examples: Simplify.
log x
x
1.) 4 4
2.) log33
x
3.) log5125
Examples: Find the inverse of each function.
x
1.) y = 4
2.) y = log6x
3.) y = ln(x + 3)
Feb 14­6:29 PM
Vertical asymptote:
Domain of a logarithmic function :
Range of a logarithmic function :
Examples: Graph. State the domain, range and V.A.
1.) y = log 2x
Feb 14­6:41 PM
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7.3 Notes.notebook
January 05, 2017
2.) y = log 2(x + 3)
3.) y = log(x - 1)
Feb 21­9:46 AM
7.3 ICE
Name: ___________________
Evaluate each logarithm.
1.) log216
2.) log88
3.) log28
4.) log5125
5.) log 10,000
6.) log93
8.) ln (1/e)
9.) log1/416
7.) log22
5
10.) log 0.001
11.) ln e
-6
12.) log4(1/16)
Feb 12­5:53 PM
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7.3 Notes.notebook
January 05, 2017
Jan 5­12:01 PM
Jan 5­11:55 AM
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