Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Sections 9.1-9.6 - Integrated Review - Functions and Properties of Logarithms: 29

Answer

$x=\frac{1}{9}$

Work Step by Step

If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$. Therefore, $log_{3}x=-2$ is equivalent to $3^{-2}=x$. We know that $x=\frac{1}{9}$, because $3^{-2}=\frac{1}{3^{2}}=\frac{1}{3\times3}=\frac{1}{9}$.
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