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**Unformatted text preview: **log(x) − log(2) = log(x + 8) − log(x + 2) 2. Solve the following inequalities analytically.
(a) x ln(x) − x > 0
x
(b) 5.6 ≤ log
≤ 7.1
10−3
x
≥ 90
(c) 10 log
10−12 (d) 2.3 < − log(x) < 5.4
1 − ln(x)
<0
(e)
x2
(f) ln(x2 ) ≤ (ln(x))2 3. Use your calculator to help you solve the following equations and inequalities.
(a) ln(x) = e−x
(b) ln(x2 + 1) ≥ 5 √
(c) ln(x) = 4 x
(d) ln(−2x3 − x2 + 13x − 6) < 0 4. Since f (x) = ex is a strictly increasing function, if a < b then ea < eb . Use this fact to solve
the inequality ln(2x + 1) < 3 without a sign diagram. Also, compare this exercise to question
4 in Section 6.3.
5. Solve ln(3 − y ) − ln(y ) = 2x + ln(5) for y .
6. In Example 6.4.4 we found the inverse of f (x) = x
log(x)
to be f −1 (x) = 10 x+1 .
1 − log(x) (a) Show that f −1 ◦ f (x) = x for all x in the domain of f and that f ◦ f −1 (x) = x for
all x in the domain of f −1 .
(b) Find the range of f by ﬁnding the domain of...

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