Download File

Section 3.4 Solving Exponential and Logarithmic Equations 239
141.
T 201 72 h
(a) 175
(b) We see a horizontal asymptote at y 20.
This represents the room temperature.
(c)
0
0
100 201 72 h
5 1 72 h
4 72 h
4
7 2h
4
ln ln 2h
7
4
ln h ln 2
7
ln47
ln 2 h
h 0.81 hour
6
142. (a)
(b)
13,387 2190.5 ln t 7250
12,000
2190.5 ln t 6137
6 18
0
ln t 2.8016
t 16.5, or 2006
(c) Let y 1 13,387 2190.5 ln t and y 2 7250.
The graphs of y 1 and intersect at t 16.5.
y 2
143. False. The equation e x 0 has no solutions.
144. False. A logarithmic equation can have any
number of extraneous solutions. For example
ln2x 1 lnx 2 lnx 2 x 5 has
two extraneous solutions, x 1 and x 3.
145. Answers will vary.
© Houghton Mifflin Company. All rights reserved.
146.
f x log a x, gx a x , a > 1.
(a)
a 1.2
−10
The curves intersect twice:
(b) If f x log a x a x gx intersect exactly once, then
x log a x a x ⇒ a x 1x .
20
−10
f
g
The graphs of y x 1x and y a intersect once for a e 1e 1.445. Then
log a x x ⇒ e 1e x x ⇒ e xe x ⇒ x e.
20
1.258, 1.258 and 14.767, 14.767
For a e 1e , the curves intersect once at e, e.
(c) For 1 < a < e 1e the curves intersect twice. For a > e 1e , the curves do not intersect.