1
f

Section 5.3
Logarithmic Functions
Objective 1:
Understanding the Definition of a Logarithmic Function
Every exponential function of the form
( )
x
f x
b
=
where
0
b
and
1
b
≠
is onetoone and thus has an
inverse function.
The graph of
( )
,
1
x
f x
b
b
=
and its inverse.
To find the equation of
1
f

:
Step 1.
Change
( )
f x
to
y
:
x
y
b
=
Step 2.
Interchange
x
and
y
:
y
x
b
=
Step 3.
Solve for
y
:
??
Before we can solve for
y
we must introduce the following definition:
Definition of the Logarithmic Function
For
0,
0and
1
x
b
b
≠
, the
logarithmic function with base
b
is defined by
log
b
y
x
=
if and only if
y
x
b
=
.
Step 3.
Solve for
y
:
y
x
b
=
can be written as
log
b
y
x
=
Step 4.
Change
y
to
1
( )
f
x

:
1
( )
log
b
f
x
x

=
5.3.1
Write the exponential equation as an equation involving a logarithm.
5.3.9
Write the logarithmic equation as an exponential equation.
( )
x
f x
b
=
(0,1)
(1, )
b
1
( 1, )
b

(1, 0)
1
( , 1)
b

( ,1)
b
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentObjective 2:
Evaluating Logarithmic Expressions
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 moshe
 Algebra, Exponential Function, Logarithmic Functions, Natural logarithm, Logarithm, logarithmic function, Common and Natural Logarithms

Click to edit the document details