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230 Chapter 3 Exponential and Logarithmic Functions<br />
55.<br />
2e 5x 18 56. 4e 2x 40<br />
57.<br />
e 5x 9<br />
e 2x 10<br />
5x ln 9<br />
2x ln 10<br />
x 1 5 ln 9<br />
x 1 2 ln 10 1.151<br />
x 0.439<br />
500e x 300<br />
e x 3 5<br />
x ln 3 5<br />
x ln 3 5 ln 5 3 0.511<br />
58.<br />
1000e 4x 75 59. 7 2e x 5<br />
60.<br />
e 4x 3 40<br />
ln e 4x ln 3<br />
40<br />
4x ln 3<br />
40<br />
x 1 4 ln 3<br />
40 0.648<br />
2e x 2<br />
e x 1<br />
x ln 1 0<br />
14 3e x 11<br />
3e x 25<br />
e x 25<br />
3<br />
ln e x ln 25 3<br />
x ln 25 3 2.120<br />
61.<br />
e 2x 4e x 5 0<br />
62.<br />
e 2x 5e x 6 0 63.<br />
250e 0.02x 10,000<br />
e x 5e x 1 0<br />
e x 2e x 3 0<br />
e 0.02x 40<br />
e x 5 or e x 1<br />
e x 2 or e x 3<br />
0.02x ln 40<br />
x ln 5 1.609<br />
e x 1 is impossible.<br />
x ln 2 0.693 or<br />
x ln 3 1.099<br />
x <br />
ln 40<br />
0.02<br />
x 184.444<br />
64.<br />
100e 0.005x 125,000 65.<br />
e x e x2 2<br />
66.<br />
e 2x e x2 8<br />
e 0.005x 1250<br />
x x 2 2<br />
2x x 2 8<br />
0.005x ln 1250<br />
x 2 x 2 0<br />
x 2 2x 8 0<br />
x <br />
ln 1250<br />
0.005<br />
x 1426.180<br />
x 2x 1 0<br />
x 2, 1<br />
x 4x 2 0<br />
x 4, 2<br />
67.<br />
e x2 3x e x2 68.<br />
x 2 3x x 2<br />
x 2 4x 2 0<br />
x 4 ± 16 8<br />
2<br />
x 2 ± 2<br />
x 3.414, 0.586<br />
e x 2 e x2 2x<br />
x 2 x 2 2x<br />
2x 2 2x 0<br />
2xx 1 0<br />
x 0, 1<br />
69.<br />
400<br />
350<br />
1 ex 1 e x 400<br />
350 8 7<br />
e x 1 7<br />
x ln <br />
1<br />
7 ln 7<br />
x ln 7 1.946<br />
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