Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

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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