Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set: 14

Answer

$x=5$

Work Step by Step

Note that: $\frac{1}{125}=\frac{1}{5^3}=5^{-3}$ Write $\frac{1}{125}$ as $5^{-3}$ to obtain: $5^{2-x}=5^{-3}$ RECALL: If $a^x = a^y$, then $x=y$. Use the rule above to obtain: $\begin{array}{cccc} \\&5^{2-x}&=&5^{-3} \\&2-x&=&-3 \\&-x&=&-3-2 \\&-x&=&-5 \\&-1(-x)&=&-5(-1) \\&x&=&5\end{array}$
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