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234 Chapter 3 Exponential and Logarithmic Functions<br />
104. lnx 1 lnx 2 ln x,<br />
ln <br />
x 1<br />
x 2 ln x x > 2<br />
x 1<br />
x 2 x<br />
x 1 xx 2 x 2 2x<br />
x 2 3x 1 0<br />
x 3 ± 9 4<br />
2<br />
Taking the positive solution, x 3 13<br />
2<br />
3 ± 13<br />
2<br />
3.303.<br />
105.<br />
log 10 8x log 10 1 x 2<br />
<br />
log 10<br />
25 ± 533<br />
4<br />
8x<br />
1 x 2<br />
8x<br />
1 x 102<br />
8x 100x 100 0<br />
2x 25x 25 0<br />
x 25 ± 252 4225<br />
4<br />
8x 100 100x<br />
Choosing the positive value, we have x 13.431 and x 180.384.<br />
106. log 10 4x log 10 12 x 2,<br />
x > 0<br />
4x<br />
log 10<br />
12 x 2<br />
4x<br />
12 x 102 100<br />
x 25x 300 0, Quadratic in x<br />
x 25 ± 252 4300<br />
2<br />
4x 1200 100x<br />
Taking the positive root and squaring, x 1146.5.<br />
<br />
25 ± 1825<br />
2<br />
107.<br />
ln 2x 2.4<br />
x 2 3 4 5 6<br />
f x 1.39 1.79 2.08 2.30 2.48<br />
6<br />
−2<br />
10<br />
−2<br />
x 5.512<br />
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