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264 Chapter 3 Exponential and Logarithmic Functions<br />
124.<br />
126.<br />
lnx 8 3 125.<br />
1<br />
lnx 8 3<br />
2<br />
lnx 8 6<br />
x 8 e 6<br />
x e 6 8 395.429<br />
log 5 x 2 log 5 x log 5 x 5 127.<br />
x <br />
log 5 x 2<br />
x log 5x 5<br />
x 2<br />
x<br />
x 2 4x 2 0<br />
4 ± 16 42<br />
2<br />
x 2 6 0.449<br />
(Other zero is extraneous.)<br />
x 5<br />
x 2 x 2 5x<br />
2 ± 6<br />
log 4 x 1 log 4 x 2 log 4 x 2<br />
log 4 x 1 log 4 x 2<br />
x 2<br />
No solution<br />
x 1 x 2<br />
x 2<br />
x 1x 2 x 2<br />
x 2 x 2 x 2<br />
x 2 0<br />
x 0<br />
log 10 1 x 1<br />
10 1 1 x<br />
(extraneous)<br />
x 1 10 1 0.9<br />
128.<br />
log 10 x 4 2 129.<br />
x 4 10 2 100<br />
x 104<br />
x 104<br />
xe x e x 0<br />
x 1e x 0<br />
x 1 0 since e x 0<br />
x 1<br />
130.<br />
132.<br />
2xe 2x e 2x 0 131.<br />
2x 1e 2x 0<br />
2x 1 0 since e 2x 0<br />
1 ln x<br />
x 2 0<br />
1 ln x 0 since x > 0<br />
ln x 1<br />
x 1 2<br />
x e 2.718<br />
x ln x x 0<br />
xln x 1 0<br />
ln x 1 0 since x > 0<br />
ln x 1<br />
x e 1 1 e 0.368<br />
133. 37550 7550e 0.0725t<br />
3 e 0.0725t<br />
ln 3 0.0725t<br />
t ln 3 15.2 years<br />
0.0725<br />
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