Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.5 - Logarithmic Functions - Exercise Set: 28

Answer

$log_{4}\sqrt[3] 4=\frac{1}{3}$

Work Step by Step

We are given that $4^{\frac{1}{3}}=\sqrt[3] 4$. If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x$ and every real number $y$. Therefore, $4^{\frac{1}{3}}=\sqrt[3] 4$ is equivalent to $log_{4}\sqrt[3] 4=\frac{1}{3}$.
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