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Review Exercises for Chapter 3 269<br />
159. True; by the Inverse Properties, log b b 2x 2x.<br />
161. False; ln x ln y lnxy lnx y<br />
160.<br />
162.<br />
e x1 e x e 1 ex<br />
e<br />
True (by Properties of exponents).<br />
lnx y lnx y<br />
False<br />
lnx y ln x ln y lnx y<br />
163. False. The domain of f x lnx is x > 0.<br />
164. True. ln <br />
x<br />
ln x ln y<br />
y<br />
165. Since 1 < 2 < 2, 2 1 < 2 2 < 2 2 ⇒ 2 < 2 2 < 4.<br />
166. (a)<br />
y 2<br />
3<br />
(b) Pattern<br />
n x i<br />
i0 i!<br />
y = e x<br />
−4<br />
y 3<br />
y 1<br />
2<br />
y 4 1 x x2<br />
2! x3<br />
3! x 4<br />
4!<br />
−1<br />
The graph of y closely approximates y e x<br />
4<br />
near 0, 1.<br />
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