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Stitz-Zeager_College_Algebra_e-book

6 a express the temperature t as a function of time t

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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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