Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.6 - Integrated Review - Functions and Properties of Logarithms: 28

Answer

$x=5$

Work Step by Step

$\log_{x}\dfrac{1}{125}=-3$ Rewrite in exponential form: $x^{-3}=\dfrac{1}{125}$ Rewrite $x^{-3}$ as $\dfrac{1}{x^{3}}$: $\dfrac{1}{x^{3}}=\dfrac{1}{125}$ If $\dfrac{1}{x^{3}}=\dfrac{1}{125}$, then $x^{3}=125$ $x^{3}=125$ Take the cubic root of both sides of the equation: $\sqrt[3]{x^{3}}=\sqrt[3]{125}$ $x=5$
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