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214 Chapter 3 Exponential and Logarithmic Functions<br />
119.<br />
2x 3 x 2 45x x2x 2 x 45 120.<br />
x2x 9x 5<br />
3x 3 5x 2 12x x3x 2 5x 12<br />
x3x 4x 3<br />
121. f g2 f 2 g2 32 2 2 3 1 8 7 15<br />
122. f g1 1 2 1<br />
123. fg6 f 6g6 36 26 3 1 20215 4300<br />
124. f g 0 2<br />
125.<br />
5x 7 x 4<br />
12<br />
1 2 126. and intersect at x 0.3<br />
y 2x 3<br />
y 8x<br />
The graphs of y 5x 7<br />
and y 2 x 4<br />
intersect when x 2.75<br />
or 11 4 .<br />
−10<br />
−4<br />
12<br />
127.<br />
3x 2 9<br />
The graphs of y 1 3x 2 and y 2 9 intersect<br />
when x 27.667 or 83 3 .<br />
128. y x 11 and y x 2 do not intersect.<br />
No solution<br />
Section 3.3<br />
Properties of Logarithms<br />
■<br />
■<br />
1. (a)<br />
You should know the following properties of logarithms.<br />
(a)<br />
(b)<br />
(c)<br />
log a x log b x<br />
log b a<br />
log a uv log a u log a v<br />
log a uv log a u log a v<br />
lnuv ln u ln v<br />
lnuv ln u ln v<br />
(d) log a u n n log a u<br />
ln u n n ln u<br />
You should be able to rewrite logarithmic expressions using these properties.<br />
Vocabulary Check<br />
1. change-of-base 2.<br />
ln x<br />
ln a<br />
3. log a u n<br />
4. ln u ln v<br />
log 5 x log 10 x<br />
log 10 5<br />
(b) log 5 x ln x<br />
ln 5<br />
2. (a)<br />
log 3 x log 10 x<br />
log 10 3<br />
(b) log 3 x ln x<br />
ln 3<br />
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