Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - Mid-Chapter Review - Mixed Review - Page 812: 20

Answer

$x=\displaystyle \frac{1}{3}$

Work Step by Step

For $x\gt 0$ and $a$, a positive constant other than 1, $\log_{a}x$ is the exponent to which $a$ must be raised in order to get $x$. Thus, $\log_{a}x=m$ means $a^{m}=x$ Here, $\log_{3}x=-1\ \ $ means$\ \ 3^{-1}=x$, and the negative exponent is interpreted as $a^{-n}=\displaystyle \frac{1}{a^{n}}$, so $x=\displaystyle \frac{1}{3}$
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