Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.3 - Logarithmic Functions - 9.3 Exercises - Page 605: 26


$\frac{1}{8}^{\frac{1}{3}}=\sqrt[3] \frac{1}{8}=\frac{1}{2}$

Work Step by Step

For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$. Therefore, $log_{\frac{1}{8}}\frac{1}{2}=\frac{1}{3}$ means the same as $\frac{1}{8}^{\frac{1}{3}}=\sqrt[3] \frac{1}{8}=\frac{1}{2}$.
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