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: 28

Answer

$x=5$

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, $log_{x}\frac{1}{125}=-3$ is equivalent to $x^{-3}=\frac{1}{125}$. We know that $x=5$, because $5^{-3}=\frac{1}{5^{3}}=\frac{1}{5\times5\times5}=\frac{1}{125}$.
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