Properties Of Natural Logarithms
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41/11/2016
Definition of the logarithmic function
For
x
0 and
b
0,
b
1
Section 8.4
The function ( ) log
f x
x
Logarithms and Logarithm
b
is a logaritmic function with a base of .
b
Functions
y
f x
( )
y
log
x
is the same as
b
x
b
Example
To change from logarithmic form to the more
Write each equation in the equivalent exponential form.
familiar exponential form, use the pattern;
x
a. 4 log x
b.
log 9
2
3
x
y
y
log
x
means
b
x
0
b
4
2
x
x
3
9
x
x
16
2
Example
Example
Write each equation in its equivalent logarithmic form.
Evaluate.
4
2
a. b
16
b. 5
x
a.
x
log 81
b.
x
log 6
c.
x
log 1
3
36
5
x
log 16 4
log
2
b
5
x
b
25
2
x
x
x
c.
0
a.
4
b.
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