5 log
3
x
−
log
3
7
30.
3 log
8
5
−
log
8
z
31.
32.
745746
Use the properties of logarithms to simplify each of the following.
33.
log
3
3
34.
log
7
7
35.
log
e
e
36.
log
10
10
37.
log
9
1
38.
log
e
1
39.
3 log
7
7 + 4 log
7
1
40.
Find x in each of the following.
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41.
log
8
x
= log
8
7
42.
log
9
x
= log
9
5
43.
log
5
(2
x
+ 7) = log
5
29
44.
log
15
26 = log
15
(3
x
−
1)
45.
log
3
1 =
x
46.
log
8
1 =
x
47.
log
7
7 =
x
48.
log
5
5 =
x
49.
log
10
x
+ log
10
25 = 2
50.
log
10
x
+ log
10
5 = 1
51.
log
2
7 = log
2
x
−
log
2
3
52.
log
5
1 = log
5
x
−
log
5
8
53.
3 log
5
x
= log
5
8
54.
1 2 log
3
x
= log
3
4
55.
log
e
x
= log
e
5 + 1
56.
log
e
x
+ log
e
7 = 2
57.
log
6
(5
x
+ 21)
−
log
6
(
x
+ 3) = 1
58.
log
3
(4
x
+ 6)
−
log
3
(
x
−
1) = 2
59.
It can be shown that
y
=
b
log
b
y
. Use this property to evaluate 5
log54
+ 3
log32
.
60.
It can be shown that
x
= log
b
b
x
. Use this property to evaluate
Cumulative Review
61.
[1.8.2]
The formula to find the volume of a cylinder is
V
=
π
r
2
h
. Find the volume of a cylinder with a radius of 2 meters and a height of 5 meters. Round your answer to the nearest tenth.
62.
[1.8.2]
Find the area of a circle whose radius is 4 meters. Round your answer to the nearest tenth.
63.
[4.1.4]
Solve the system.
5
x
+ 3
y
= 9
7
x
−
2
y
= 25
64.
[4.2.2]
Solve the system.
2
x
−
y
+
z
= 3
x
+ 2
y
+ 2
z
= 1
4
x
+
y
+ 2
z
= 0
746747
At the end of 2010, a study ranked the top ten cities where households owed the highest percent of their average yearly income to credit card companies. Below is the information for Wilmington, North Carolina (ranked #1), and Toled
65.
[0.5.4; 5.2.2]
Wilmington, North Carolina
Number of households: 1.53 × 10
5
Total credit card debt for all households: +1.117 × 10
9
Average yearly household income: $42,392
66.
[0.5.4; 5.2.2]
Toledo, Ohio
Number of households: 2.56 × 10
5
Total credit card debt for all households: +1.9 × 10
9
Average yearly household income: $44,349
Quick Quiz 12.3
1.
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Express
as a sum or difference of single logarithms.
2.
Express 3 log
6
x
+ log
6
y
−
log
6
5 as a single logarithm.
3.
Find
x
if
4.
Concept Check
Explain how you would simplify log
10
(0.001).
747748
How Am I Doing? Sections 12.1–12.3
How are you doing with your homework assignments in Sections 12.1 to 12.3? Do you feel you have mastered the material so far? Do you understand the concepts you have covered? Before you go further in the textbook, take some ti
12.1
1.
Sketch the graph of
f
(
x
) = 2
−
x
. Plot at least four points.

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