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222 Chapter 3 Exponential and Logarithmic Functions
97. ––CONTINUED––
(c)
lnT 21 0.0372t 3.9971,
linear model
(d)
0.07
T 21 e 0.0372t3.9971
10
T 21 54.4e 0.0372t
21 54.40.964 t
0
0
1
0.00121t 0.01615,
T 21
30
linear model
0
0
30
T 21
1
0.00121t 0.01615
T 21
1
0.00121t 0.01615
80
0
20
30
98. If y ab x , then ln y lnab x ln a x ln b,
which is linear. If y 1 then 1 cx d.
cx d , y
99. True
100. False. For example, let x 2 and a 1.
101. False. For example, let x 1 and a 2.
Then fx a ln2 1 0, but
Then
But fx
fx fa ln2 ln 1 ln 2.
f a x ln 1 2 . fa ln 1
ln 2 0.
102. False. For example, let x 1 and a 1.
Then fx a ln1 1 ln 2, but
fxfa ln 1ln 1 0.
103. False. ln x 1 2 ln x
In fact, ln x 12 1 2 ln x.
104. False. For example, let n 2 and x e.
105. True. In fact, if ln x < 0, then 0 < x < 1.
Then fx n ln e 2 1, but
nfx 2 ln e 2.
106. False. For example, let x e.
Then fx lne 1 2 ln e 1 2 > 0, but e < e.
107. Let and , then a y x
a
y log a x z log ab x
and
1 b z a yz
1
a
yzz
b
log a 1 b y z
z
b z
y z 1 ⇒ 1 log a 1 b log a x
log ab x .
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