Exponential Functions And Logarithms Worksheet Page 2
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1
2
3
4How to write logarithmic equations in exponential equation form:
Additional Properties of Logs
1.
log
1
0
because:
=
b
2.
log
b
1
because:
=
b
x
3.
because:
log
b
x
=
b
log
x
4.
b
x
b
=
x
y
5. If
b
b
, then
x
y
=
=
Example #1: Express in exponential form.
a. log
8 = 3
b. log100 = 2
c. log0.001 = -3
2
Example #2: Express in logarithmic form.
3
2
−
1
4
a. 2
= 16
b.
c.
27
16
8
4
3
=
=
9
Example #3: Evaluate the following.
1
a. log
36
b. log
c. log
3
3
6
2
3
16
Example #4: Solve the following.
a. log
x = -4
b. log
x = 2
c. log
8 = x
3
5
2
Example #5: Find the base of each logarithm.
1
⎛
⎞
a. log
16 = 4
b. log
4 = 1
c. log
= 2
⎜
⎟
x
x
x
64
⎝
⎠
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