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: 20

Answer

$\frac{1}{7}ln(x)$

Work Step by Step

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, $ln(\sqrt[7] x)=ln(x^{\frac{1}{7}})=\frac{1}{7}ln(x)$. Recall that $ln(x)$ is a natural logarithm with an understood base of $e$.
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