344 CHAPTER 5 Exponential and Logarithmic Functions Explaining Concepts 119. Fill in the reason for each step in the following two solutions. Solve: ( ) − = x log 1 2 3 2 Solution A Solution B ( ) − = x log 1 2 3 2 ( ) − = x log 1 2 3 2 ( ) − = = x 1 3 9 2 2 ( ) − = x 2 log 1 2 3 ( ) − = ± x 1 3 ( ) − = x log 1 1 3 − = − x 1 3 or − = x 1 3 − = = x 1 3 3 1 = − x 2 or = x 4 = x 4 Both solutions given in Solution A check. Explain what caused the solution = − x 2 to be lost in Solution B. ‘Are You Prepared?’ Answers 1. { } −3, 10 2. { } −2, 0 3. { } −1.43 4. { } −1.77 Problems 120–129 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. Retain Your Knowledge 120. Solve: + − + = x x x 4 3 25 6 0 3 2 121. Determine whether the function is one-to-one: ( ) ( ) { } ( ) ( ) − − 0, 4, 2, 2, 4,0, 6,2 122. For ( ) = − f x x x 2 and ( ) = + − g x x x 5 3 , find f g. Then find the domain of f g. 123. Find the domain of ( ) = + + − f x x x 3 1. 124. Solve: − + = x x 7 5 125. If y is inversely proportional to the square of x and = y 2.16 when = x 5, find y when = x 3. 126. If ( ) = − f x x x 2 and ( ) = + g x x 5 2 , find ( )( ) + f g x . 127. Find the distance between the center of the circle ( ) ( ) − + + = x y 2 3 25 2 2 and the vertex of the parabola ( ) = − − + y x 2 6 9. 2 128. Find the average rate of change ( ) = f x x log2 from 4 to 16. 129. Rationalize the numerator: + − x x 6 6 (e) At what price are the ratings of the two wines equal? What is the rating of the wine at this price? (f) Explain the effect of the coefficients for each of the two (expert and nonexpert) models. Source: Goldstein, Robin et al. (2008) Do More Expensive Wines Taste Better? Evidence from a Large Sample of Blind Tastings. Journal of Wine Economics, Vol. 3, Number 1, Spring 2008. Challenge Problems In Problems 116–118, solve each equation. Express irrational solutions in exact form. 116. ( ) = x x ln ln 2 2 117. = x log 2log 3 118. + − = x 4 128 0 x x (log ) log 4 2 4
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