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LOGARITHM TEST REVIEW
Graph each of the following.
1. y  log 4 x
2.
f ( x)  log 1 x
3
Find the inverse of each of the following.
F1 I
y  GJ
H9 K
x
3. y = 7
x
4.
f ( x )  log 9 x
5.
6.
f ( x )  log w x
7. y = zx
Write the exponential equation in logarithmic form.
8. 34 = 81
9. 4
1
12.
16 2 
1
4
3

3
1
16
10.
9 2  27
11. ab =12
1
13.
72  7
14. mn = p
Write the logarithmic equation in exponential form.
15. log 3 9  2
16. log 5 25 
1
2
1
 2
b2
20. log11 11 
Solve each equation.
22. log 3 x  2
23. log x 16  4
19. logb
26. log 64
30.
1
y
8
27. log x
2
log 1 (4 x  7)  2
17. log x y  4
1
2
1
4
18. log8 4 
2
3
21. log a b  c
24. log 4 x  2
28.
log 1 8  y
25. log 8 32  x
29. log16 ( 3x  1) 
2
31. log 3 (2 y  3)  log 3 ( y  6)
3
32.
log5 ( x 2  2)  log5 (10x  18)
33.
log2 ( x 2  14 x)  5
Use the laws of logarithms to expand each expression.
34. log 3 mn
35.
log 4 a 3b
36. log 1 ( ab)
3
37. log 7
xy
2
m
n
38. log 3
3
x5
39. log 2 3
y
3
Fx I
40. log GJ
Hy K
42. log a b c
43. log 2a b
Use the laws of logarithms to rewrite as a single logarithm.
4
6
41. log 5 4 x
1
2
44. log p  log q
45. 4 logb
48. 3(log a  log b)
49.
46. 2 log a  3 log b
1
log a  6 log b
3
47. log a  3 log b
50. log a  4 log b  2 log c
Solve each equation.
51. log 4 8  log 4 3  log 4 6 x
54. log 7 x  3 log 7 2
57. log 7 x 
53. log x  log
52. 2 log 5  log n
55. 4 log5 x  log5 4  log5 4
1
1
log 7 144  log 7 8
2
3
56. log 4 ( x  3)  log 4 ( x  3)  2
58. log5 ( x  3)  log5 x  log5 4
Evaluate each of the following to the nearest ten-thousandth.
59. log 2 15
60. log 7 21
61. log 3 5
Solve for x to the nearest hundredth.
62.
3x  39
63.
287  4 x
64.
7 x  3  20
65.
32 x1  54
66.
53x  263
67.
43 x2  801
68.
4 x  187
.
69.
52 x  34 x 1
70.
4 x  63x 7
ANSWER KEY
1
 log 20
4
y = 4x
1. x
-3
-2
-1
0
1
2
3
y
1/64
1/16
¼
1
4
16
64
3. y-1 = log7x
8. 4 = log3 81
12.
1
1
= log16
4
2
15. 3
2
=
9
19. b-2 =
1
b2
y = log4x
y = (1/3)x
y = log1/3x
x
y
1/64 -3
1/16 -2
¼
-1
1
0
4
1
16
2
64
3
2. x
-3
-2
-1
0
1
2
3
x
27
9
3
1
1/3
1/9
1/27
4. f-1(x) = 9x
5. y-1 = log1/9x
9. -3 = log4
13.
1
16
1
= log7 7
2
1
2
16.
5  25
20.
112  11
10.
y
27
9
3
1
1/3
1/9
1/27
6. f-1(x) = wx
3
= log9 27
2
7. y-1 = logzx
11. b = loga 12
14. n = logm p
4
17. x = y
1
21. ac = b
18.
y
-3
-2
-1
0
1
2
3
2
3
8 4
22. x = 9
23. x = 2
24. x =
1
16
25. x =
5
3
26. y =
1
2
27. x = 4
28. y = -3
29. x = 1
30. x =
1
2
31. y = 9
32. x =8 or x = 2
33. x = -2 or x = 16
34. log 3 m  log 3 n
35. 3 log 4 a  log 4 b
36.
3 log 1 a  3 log 1 b
2
37.
1
log 7 x  log 7 y
2
40. 4 log 6 x  4 log 6 y
38.
1
log 3 m  log 3 n
2
39. 5 log 2 x  3 log 2 y
41.
1
log 5 x
4
42. 3 log a  log b 
45.
logb 4
46.
48.
Fa I a
logGJor log
Hb K b
43. log 2  3 log a  log b
44. log pq
a
47. log 3
b
3
log a 2b 3
3
3
3
49. log
a
b6
ab 4
50. log 2
c
51. x = 4
52. n = 25
53. x = 5
54. x = 8
55. x = 2
56. x = 5
57. x = 6
58. x = 1
59. 3.9069
60. 1.5646
61. 1.4650
62. x = 3.33
63. x = 4.08
64. x = 1.46
65. x = 1.32
66. x = 1.15
67. x = 2.27
68. x = .45
69. x = .93
70. x = -3.14
2
1
log c
2