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228 Chapter 3 Exponential and Logarithmic Functions
17.
4 x 16 18. 3 19. 5 x 1
x 243 20.
625
4 x 4 2
3 x 3 5
5
x 2
x 1 x 5
5 4 54
x 4
7 x 1 49
7 x 7 2
x 2
21.
1 8 x 64 22.
23.
8 x 8 2
x 2
x 2
1 2 x 32 2 3 x 81
16
24.
1 2 x 1 2 5
3 2 x 3 2 4
x 5
x 4
x 4
3 4 x 27
64
3 4 x 3 4 3
x 3
25.
27.
610 x 216 26.
10 x 36
log 10 10 x log 10 36
x log 10 36 1.5563
2 x3 256 Alternate solution:
28.
2 x 2 3 256
2 x3 2 8
2 x 32
x 3 8
x 5
x 5
58 x 325
8 x 65
x log 8 65
3 x1 1 81
3 x1 3 4
x 1 4
ln 65
ln 8 2.0075
x 3
29.
ln x ln 5 0
30.
ln x ln 2 0 31. ln x 7
32.
ln x 1
ln x ln 5
ln x ln 2
x e 7
e 1 x
x 5
x 2
x 1 e 0.368
33.
36.
log x 625 4 34. log x 25 2
35.
x 4 625
x 4 5 4
x 5
log 10 x 1 2
x 10 12 1
10
0.316
37.
x 2 25
x 5
ln2x 1 5
2x 1 e 5
x 1 e5
2
74.707
38.
log 10 x 1
x 10 1
x 1 10
ln3x 5 8
e 8 3x 5
x 1 3 e8 5
991.986
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39. ln e x2 x 2 ln e x x 2 40. ln e 2x1 2x 1 41. e ln5x2 5x 2 42. e ln x2 x 2
43. 1 ln e 2x 1 2x 2x 1 44. 8 e ln x3 8 x 3 x 3 8