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Section 3.4 Solving Exponential and Logarithmic Equations 229
45.
8 3x 360 46.
6 5x 3000 47.
5 t2 0.20 1 5
ln 8 3x ln 360
3x ln 8 ln 360
ln 6 5x ln 3000
5x ln 6 ln 3000
t 2 ln 5 ln 1 5
3x
ln 360
ln 8
5x
ln 3000
ln 6
t ln 5 ln 5
2
x 1 3
ln 360
ln 8
x
ln 3000
5 ln 6 0.894
t
2 1
x 0.944
t 2
48.
4 3t 0.10 49.
52 3x 13 100 50.
68 2x 15 2601
ln 4 3t ln 0.10
52 3x 113
68 2x 2586
3t ln 4 ln 0.10
3t
ln 0.10
ln 4
ln 0.10
t
3 ln 4 0.554
2 3x 113
5
ln 2 3x ln
113
5
3 x ln1135
ln 2
x 3 ln1135
ln 2
8 2x 431
2 x ln 8 ln 431
2 x
ln 431
ln 8
x 2
x 4.917
ln 431
ln 8
x 1.498
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51.
53.
1 0.10
12 12t 2 52.
12.1
12 12t 2
12t ln
12.1
12 ln 2
t 1 12
t 6.960
ln 2
ln12.112
0.878
16
26 3t 30
3t ln 16 0.878
26 ln 30
5000
1 0.005 x
0.005 250,000 54. 1 0.01
250 x
0.01 150,000
50001.005 x 1250
2501.01 x 1500
1.005 x 0.25
1.01 x 6
x ln1.005 ln 0.25
x ln 1.01 ln 6
ln 0.25
x x ln 6
ln1.005
ln 1.01
x 277.951
x 180.070
ln 30
t
3 ln 16 0.878
26
3.4012
8.3241 0.409