Logarithm Worksheet With Answer Key - Blake Farman, University Of South Carolina Page 2
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2
3
4
52
BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA
3
Solution. (a) If we write 27 = 3
, then by the laws of logarithms we have
1
3
log
= log
(1)
log
(27) = 0
log
(3
) =
3.
3
3
3
3
27
,
1
(b) If we write
10 = 10
we have
2
1
1
log
( 10) = log
(10
=
.
2
10
10
2
2
1
(c) First, write 0.2 =
=
so that by the laws of logarithms
10
5
1
log
(0.2) = log
= log
(1)
log
(5) = 0
1 =
1.
5
5
5
5
5
32. Express the equation in exponential form.
(a) log
(81) = 4,
3
1
(b) log
.
2
8
4
Solution. (a) The equation log
(81) = 4 is true if and only if 3
= 81, which is the exponential
3
form.
1
1
3
(b) The equation log
=
3 is true if and only if 2
=
.
2
8
8
34. Express the equation in logarithmic form.
3
(a) 10
= 1000,
1/2
(b) 81
= 9.
3
Solution. (a) The equation 10
= 1000 tells us that log
(1000) = 3.
10
1/2
1
(b) The equation 81
= 9 tells us that log
(9) =
.
81
2
4.2
10. Evaluate the given expression.
(a) log
(4) + log
(25),
10
10
(b) log
(160)
log
5,
2
2
1
(c)
log
(64).
2
2
Solution. (a) Using the law for multiplication we have
2
log
(4) + log
(25) = log
(4 25) = log
(100) = log
(10
) = 2.
10
10
10
10
10
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