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260 Chapter 3 Exponential and Logarithmic Functions<br />
61.<br />
hx 1 2 ln x<br />
3<br />
62. fx 1 4 ln x<br />
Domain:<br />
3<br />
Domain: x > 0<br />
Vertical asymptote:<br />
x-intercept: 1, 0<br />
x 0<br />
−1<br />
−3<br />
8<br />
0, <br />
Vertical asymptote:<br />
Intercept: 1, 0<br />
x 0<br />
0<br />
−3<br />
9<br />
63.<br />
18,000<br />
t 50 log 10<br />
18,000 h<br />
(a) 0 ≤ h < 18,000<br />
(c) The plane climbs at a faster rate as it approaches<br />
its absolute ceiling.<br />
(d) If h 4000, t 50 log 10<br />
18,000<br />
5.46 minutes.<br />
18,000 4000<br />
(b)<br />
100<br />
0<br />
0<br />
20,000<br />
Vertical asymptote: h 18,000<br />
64.<br />
t 12.542 ln <br />
x<br />
x 1000 , x > 1000 66.<br />
(a) For x 1254.68, t 20 years.<br />
(b) For x 1254.68, t 20, the total amount paid is 1254.682012 $301,123.20.<br />
The interest is 301,123.20 150,000.00 $151,123.20.<br />
65. log 4 9 log 10 9<br />
log 10 4 1.585<br />
log 4 9 ln 9<br />
ln 4 1.585<br />
log 12 5 log 10 5<br />
log 10 12 2.322<br />
log 12 5 ln 5<br />
ln12 2.322<br />
67.<br />
log 12 200 log 10 200<br />
log 12 200 <br />
log 10 12 2.132 68.<br />
ln 200<br />
ln 12 2.132<br />
log 3 0.28 <br />
log 3 0.28 log 10 0.28<br />
log 10 3 1.159<br />
ln 0.28<br />
ln 3 1.159<br />
69. fx log 2 x 1 <br />
4<br />
−1 11<br />
−4<br />
lnx 1<br />
ln 2<br />
70.<br />
fx 2 log 3 x 2 ln x<br />
ln 3<br />
7<br />
−1 11<br />
−1<br />
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