Download Objective: Students will be able to convert equations between

3.3 Logarithmic Functions and Their Graphs
Name: ___________________
Objective: Students will be able to convert equations between
logarithmic form and exponential form, evaluate common and
natural logarithms and graph them.
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:
logby=x
if and only if bx=y
In words: logby=x is read "log base b of y".
Common log: log10x=logx
Natural log: logex=lnx
Feb 14­6:15 PM
Examples: Rewrite in exponential form.
1.) log28=3
2.) log41=0
3.) log1212=1
4.) log2¼=-2
Examples: Rewrite in logarithmic form.
1.) 32=9
2.) 5-2=1/25
3.) (½)-3=8
4.) 40=1
Examples: Evaluate the logarithms.
1.) log525
2.) log381
Feb 14­6:26 PM
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3.) log100
4.) log1/327
5.) lne4
6.) log91
7.) log√10
8.) log4(1/64)
Inverse Functions: The logarithmic function
y = logbx and the exponential function y = bx are
inverses. This means: logbbx=x and blogbx=x.
Examples: Simplify.
1.) 4log4x
2.) log33x
3.) log5125x
4.) elnπ
Feb 14­6:29 PM
Let's talk about log(-10)...
Examples Use a calculator to evaluate the expression, if it is
defined.
1.) log(.908)
Examples Solve.
1.) log3x = 2
2.) log(-5.14)
3.) ln7
2.) logx = -4
Oct 10­6:22 PM
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Recall this wonderful function: f(x) = lnx
Domain:
Range:
Continuity:
Increasing/decreasing behavior:
Symmetry:
Boundedness:
Extrema:
H.A.
V.A.
End behavior:
Oct 10­6:27 PM
Examples: Graph. State the domain, range and V.A.
2.) f(x) = 2ln(-x) + 3
1.) f(x) = -ln(x+2)
Feb 14­6:41 PM
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3.) g(x) = log2x
4.) f(x) = log2(x -2)
Feb 21­9:46 AM
So...what are logarithms good for, anyways???
The level of sound intensity in decibels (dB) is β=10log(I/I0),
where β is the number of decibels, I is the sound intensity in W/m2,
and I0 = 10-12 W/m2 is the threshold of human hearing (the
quietest audible sound intensity).
Example: A subway train has a sound intensity of 10-2 W/m2.
How loud is the train?
Assignment: Pages 308-309: 1-35 odd, 37-40, 41, 49, 56, 59, 60
Oct 10­6:34 PM
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