## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 488: 14

#### Answer

Solution set = $\{5\}.$

#### Work Step by Step

$5^{2-x}=\displaystyle \frac{1}{125} \qquad$... Recognize 125 as a power of 5 $5^{2-x}=\displaystyle \frac{1}{5^{3}} \qquad$... apply $a^{-n}=\displaystyle \frac{1}{a^{n}}$ $5^{2-x}=5^{-3}\qquad$... if $a^{m}=a^{n}$, then $m=n$ $2-x=-3\qquad$... add $x+3$ $2+3=x$ $x=5$ Solution set = $\{5\}.$

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