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 9.3 - Logarithmic Functions - Exercise Set: 25

Answer

$x=-1$

Work Step by Step

First, we let $\log_{5}{\frac{1}{5}} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=\frac{1}{5}$ and b=5, to obtain: $5^x=\frac{1}{5}$ Write $\frac{1}{5}$ as $ 5^{-1}$ to obtain: $5^x=5^{-1}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=-1$
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