Download File

226 Chapter 3 Exponential and Logarithmic Functions
5.
6.
log 4 3x 3 (a) x 21.3560 is an approximate solution.
4 3 3x
x 64 3 21.333
(b) No, x 4 is not a solution.
(c) Yes, x 64 3 is a solution.
log 6 5 3 x 2 ⇔ ln 5 3x
ln 6 2
ln 5 3 20.2882
(a) x 20.2882;
1.965 2; No
ln 6
(b) x 108 log 6 5 Yes
3 108
5 log 636 2;
5 ; ln 5
(c) x 7.2;
37.2
1.3869 2; No
ln 6
7.
lnx 1 3.8
(a)
x 1 e 3.8
(c)
x 1 ln 3.8
ln1 e 3.8 1 ln e 3.8 3.8
ln1 ln 3.8 1 lnln 3.8 0.289
Yes, x 1 e 3.8 is a solution.
No, x 1 ln 3.8 is not a solution.
(b)
x 45.7012
ln45.7012 1 ln44.7012 3.8
Yes, x 45.7012 is a solution.
8.
ln2 x 2.5
(a)
(b)
x e 2.5 2; ln2 e 2.5 2 ln e 2.5 2.5; Yes
x 4073
4073
400 ; ln2 400 2.5; Yes
(c)
x 1 2 ; ln2 1 2 0.9163 2.5; No
9.
11
g
f
−9
9
−1
Point of intersection: 3, 8
Algebraically: 2 x 8
2 x 2 3
x 3 ⇒ y 8 ⇒ 3, 8
10.
fx gx
27 x 9
27 x 27 23
x 2 3
Point of intersection:
10
g
f
−9
9
−2
2 3, 9
© Houghton Mifflin Company. All rights reserved.