Section 8.5
Logarithmic Functions
829
8.5 Exercises
1
In Exercises 1-18, find the exact value
of the function at the given value b.
√
1. f (x) = log3 (x); b = 5 3.
In Exercises 19-26, use a calculator to
evaluate the function at the given value
p. Round your answer to the nearest
hundredth.
2.
f (x) = log5 (x); b = 3125.
19.
f (x) = ln(x); p = 10.06.
3.
f (x) = log2 (x); b =
20.
f (x) = ln(x); p = 9.87.
4.
f (x) = log2 (x); b = 4.
21.
f (x) = ln(x); p = 2.40.
5.
f (x) = log5 (x); b = 5.
22.
f (x) = ln(x); p = 9.30.
6.
f (x) = log2 (x); b = 8.
23.
f (x) = log(x); p = 7.68.
7.
f (x) = log2 (x); b = 32.
24.
f (x) = log(x); p = 652.22.
8.
f (x) = log4 (x); b =
1
.
16
25.
f (x) = log(x); p = 6.47.
26.
f (x) = log(x); p = 86.19.
9.
1
f (x) = log5 (x); b =
.
3125
1
.
16
10.
f (x) = log5 (x); b =
11.
f (x) = log5 (x); b =
12.
f (x) = log3 (x); b =
13.
f (x) = log6 (x); b =
14.
f (x) = log5 (x); b =
15.
f (x) = log2 (x); b =
16.
1
.
25
√
6
5.
√
3
3.
√
6
6.
√
5
5.
√
6
2.
In Exercises 27-34, solve the given equation, and round your answer to the nearest hundredth.
27.
13 = e8x
28.
2 = 8ex
29.
19 = 108x
30.
17 = 102x
31.
7 = 6(10)x
1
f (x) = log4 (x); b = .
4
32.
7 = e9x
17.
1
f (x) = log3 (x); b = .
9
33.
13 = 8ex
18.
f (x) = log4 (x); b = 64.
34.
5 = 7(10)x
Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/
Version: Fall 2007
830
Chapter 8
Exponential and Logarithmic Functions
In Exercises 35-42, the graph of a logarithmic function of the form f (x) =
logb (x − a) is shown. The dashed red
line is a vertical asymptote. Determine
the domain of the function. Express your
answer in interval notation.
38.
y
5
5
x
35.
y
5
39.
5
x
y
5
5
x
36.
y
5
40.
5
x
y
5
5
x
37.
y
5
41.
5
x
y
5
5
Version: Fall 2007
x
Section 8.5
Logarithmic Functions
831
42.
y
5
5
x
Version: Fall 2007
832
Chapter 8
8.5 Answers
1.
1
5
3.
−4
5.
1
7.
5
9.
−5
11.
1
6
13.
1
6
15.
1
6
17.
−2
19.
2.31
21.
0.88
23.
0.89
25.
0.81
27.
0.32
29.
0.16
31.
0.07
33.
0.49
35.
(0, ∞)
37.
(−1, ∞)
39.
(0, ∞)
41.
(−3, ∞)
Version: Fall 2007
Exponential and Logarithmic Functions