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Section 3.4 Solving Exponential and Logarithmic Equations 233<br />
94.<br />
log 10 x 2 6 95.<br />
7 log 4 0.6x 12<br />
96.<br />
4 log 10 x 6 11<br />
x 2 10 6<br />
x ±10 6 ±1000<br />
log 4 0.6x 12<br />
7<br />
4 127 0.6x 3 5x<br />
log 10 x 6 11 4<br />
10 114 x 6<br />
x 5 3 4127<br />
x 6 10 114<br />
17.945<br />
568.341<br />
97.<br />
lnx 2 1<br />
98.<br />
lnx 8 5<br />
99.<br />
lnx 1 2 2<br />
x 2 e 1<br />
1<br />
2lnx 8 5<br />
e lnx12 e 2<br />
x 2 e 2<br />
lnx 8 10<br />
x 1 2 e 2<br />
x e 2 2 5.389<br />
e 10 x 8<br />
x 1 e or x 1 e<br />
x 8 e 10<br />
x e 1 1.718<br />
22,034.466<br />
or<br />
x e 1 3.718<br />
100.<br />
lnx 2 1 8<br />
101.<br />
log 4 x log 4 x 1 1 2<br />
e 8 x 2 1<br />
x ±e 8 1 ±54.589<br />
x<br />
log 4x 1 1 2<br />
4 log 4xx1 4 12<br />
x<br />
x 1 2<br />
x 2x 1<br />
x 2x 2<br />
2 x<br />
© Houghton Mifflin Company. All rights reserved.<br />
102.<br />
log 3 x log 3 x 8 2 103.<br />
log 3 xx 8 2<br />
x 2 8x 9 0<br />
x 9x 1 0<br />
x 9<br />
x 1 is extraneous.<br />
3 2 xx 8 x 2 8x<br />
lnx 5 lnx 1 lnx 1<br />
lnx 5 ln <br />
x 1<br />
x 1<br />
x 5 x 1<br />
x 1<br />
x 5x 1 x 1<br />
x 2 6x 5 x 1<br />
x 2 5x 6 0<br />
x 2x 3 0<br />
x 2 or x 3<br />
Both of these solutions are extraneous, so the<br />
equation has no solution.
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