Solving Logarithmic Equations Worksheet With Answer Key
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1
2
3
4Solving Logarithmic Equations
Example 1
Write each equation in exponential form.
3
1
a. log
8 =
b. log
3 =
32
81
5
4
2
1
The base is 32, and the exponent is
3 .
The base is 81, and the exponent is
4 .
3
1
8 =
32
3 =
81
5
4
Example 2
Write each equation in logarithmic form.
4
a. 6
= 1296
1
-8
b. 2
=
The base is 6, and the exponent, or
256
logarithm, is 4.
The base is 2, and the exponent, or
log
1296 = 4
logarithm, is -8.
6
1
log
256 = -8
2
Example 3
1
Evaluate the expression log
.
3
27
1
Let x = log
27 .
3
1
x = log
3
27
1
x
3
=
Definition of logarithm
27
1
x
-1
-m
3
= (27)
a
=
m
a
x
3
-1
3
3
= (3
)
3
= 27
x
-3
m
n
mn
3
= 3
(a
)
= a
u
v
x = -3
If a
= a
, then u = v.
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