Section 5.5
Exponential and Logarithmic Equations
Definition of the Logarithmic Function
For
0,
0and
1
x
b
b
≠
,
if
log
b
y
x
=
, then
y
x
b
=
, and if
y
x
b
=
, then
log
b
y
x
=
.
The Logarithm Property of Equality
For
0,
1,
b
b
≠
0
u
, and
0
v
,
if
log
log
b
b
u
v
=
, then
u
v
=
, and if
u
v
=
, then
log
log
b
b
u
v
=
.
Properties of Logarithms
For
0,
1,
b
b
≠
0
u
, and
0
v
,
log
log
log
b
b
b
uv
u
v
=
+
Product Rule for Logarithms
log
log
log
b
b
b
u
u
v
v
=

Quotient Rule for Logarithms
log
log
b
b
r
u
r
u
=
Power Rule for Logarithms
Change of Base Formula
For any positive base
1
b
≠
and for any positive real number
u
, then
log
log
log
a
b
a
u
u
b
=
where
a
is any positive number such that
1
a
≠
.
Note that the preferred choices for
a
are 10 and
e.
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View Full DocumentObjective 1:
Solving Exponential Equations
Solving Exponential Equations
If the equation can be written in the form
u
v
b
b
=
(relating the bases), then solve the equation
=
u
v
.
If the equation can be written in the form
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 Spring '09
 moshe
 Algebra, Logarithmic Equations, Equations, Derivative, Exponentiation, Logarithm

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