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: 28

Answer

$x=-2$

Work Step by Step

First, we let $\log_{3}{\frac{1}{9}} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=\frac{1}{9}$ and $b=3$, to obtain: $3^x=\frac{1}{9}$ Write $\frac{1}{9}$ as $ 3^{-2}$ to obtain: $3^x=3^{-2}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $x=-2$
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