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Logarithms
Chapter 10
Objective
 You will be able to define a logarithm and
convert from an exponential to a log and
vice versa.
 You will analyze basic logs and evaluate
whether they exist or not.
 If the function cannot be solved and:
 … it is in Exponential Form then switch it to
Logarithmic Form
 … it is in Logarithmic Form then switch it to
Exponential Form
What is a Log?
 A logarithm is an exponent.
 2x=y is an exponential.
 List the Domain and the Range.
Find the Inverse
x = 2y
y = 2x
x
f(x)
x
f(x)
-2
-1
0
1
2
1/4
1/2
1
2
4
1/4
1/2
1
2
4
-2
-1
0
1
2
PLOT the coordinates on the same set of axes.
Inverse
Log
 But we can’t re-solve x = 2y for y.
So mathematicians developed the
logarithm as the inverse of the
exponential.
The Logarithm is the exponent
which makes the equation
(function) true.
Equivalent forms.
 y = 2x is equal to log2 y = x.
 Rewrite y = 2x as 2x = y.
 SNAIL to change between
forms.
Log2 Y
 2x = y
Head is
base of
the
Base > 0; Base
1
Log
The
answer
=x
Exponent
Now Try to change forms
Try and change more …
2