College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3: 64

Answer

$log_{4}(\sqrt[3] \frac{x}{y})$

Work Step by Step

Based on the quotient rule of logarithms, we know that $log_{b}(\frac{M}{N})=log_{b}M-log_{b}N$ (where $b$, $M$, and $N$ are positive real numbers and $b\ne1$). Therefore, $\frac{1}{3}(log_{4}(x)-log_{4}(y))=\frac{1}{3}log_{4}(\frac{x}{y})$. According to the power rule of logarithms, we know that $log_{b}M^{p}=plog_{b}M$ (when $b$ and $M$ are positive real numbers, $b\ne1$, and $p$ is any real number). Therefore, $\frac{1}{3}log_{4}(\frac{x}{y})=log_{4}(\sqrt[3] \frac{x}{y})$.
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