Thomas Calculus 13th [Solutions]

Chapter 1 Additional and Advanced Exercises 57
27.
ln x
log4
x ln 4 ln x ln 2 ln 2 ln 2 1
log2
x ln x
ln 2
ln 4 ln x ln 4 2ln 2 2
28. (a) f ( x) ln 2 , g( x) ln x
ln x ln 2
(b) f is negative when g is negative, positive
when g is positive, and undefined when
g = 0; the values of f decrease as those of g
increase.
(c)
ln 2 ln x 2 2
(ln 2) (ln x)
ln x ln 2
(ln 2 ln x)(ln 2 + ln x) = 0 ln x = ln 2
ln x ln 2
or ln x = ln 2 e e or
ln x ln(1/2)
e e x = 2 or x 1
2 .
Therefore, the two curves cross at the two
ln(1/2)
points 1 , 1 , 1 and
2 ln 2 2
2, ln 2 (2, 1).
ln 2
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