Logarithm Worksheet With Answer Key - Blake Farman, University Of South Carolina Page 5
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5MATH 111:
HOMEWORK 08 SOLUTIONS
5
(a)
2 log
(x + 1) + 2 log
(x
1) = 2(log
(x + 1) + log
(x
1))
8
8
8
8
= 2(log
((x + 1)(x
1)))
8
2
= 2(log
(x
1))
8
2
2
= log
((x
1)
)
8
4
2
= log
(x
2x
+ 1).
8
(b)
2
x
1
(x + 1)(x
1)
2
log
(x
1)
log
(x
1) = log
= log
= log
(x + 1).
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5
5
5
5
x
1
x
1
34. Use the change of base formula and a calculator to evaluate the logarithm.
(a) log
(16),
3
(b) log
(92).
6
Solution. Using the change of base formula and a calculator we have
(a)
log
(16)
10
log
(16) =
2.523719.
3
log
(3)
10
(b)
log
(92)
10
log
(92) =
2.523658.
6
log
(6)
10
36. Use the change of base formula and a calculator to evaluate the logarithm.
(a) log
(125),
4
(b) log
(2.5).
12
Solution. Using the change of base formula and a calculator we have
(a)
log
(125)
10
log
(125) =
3.482892.
4
log
(4)
10
(b)
log
(2.5)
10
log
(2.5) =
0.368743.
12
log
(12)
10
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