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 4.2: 104

Answer

$x=16$

Work Step by Step

From the definition of the logarithmic function on page 456, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (for $x\gt0$, $b\gt0$, and $b\ne1$). Therefore, $log_{64}x=\frac{2}{3}$ is equivalent to $64^{\frac{2}{3}}=x$ in logarithmic form. We know that $64^{\frac{2}{3}}=\sqrt[3] 64^{2}=(\sqrt[3] 64)^{2}=(4)^{2}=16$. So, $x=16$.
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