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