Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 296: 94

Answer

$x=\frac{1}{2}$

Work Step by Step

We know that if $\log_a{y}=x$ then $a^x=y$. Hence, if $\log_x{\left(\frac{1}{8}\right)}=3$, then $x^3=\frac{1}{8}$ Solve the equation above to obtain: $x^3=\left(\frac{1}{2}\right)^3\\ \sqrt[3]{x^3}=\sqrt[3]{\left(\frac{1}{2}\right)^3}\\ x=\frac{1}{2}$.
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