Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.7 - Common Logarithms, Natural Logarithms, and Change of Base - Practice - Page 886: 9

Answer

$\frac{1}{3}$

Work Step by Step

$\ln \sqrt[3] e$ can be rewritten as $\ln e^{\frac{1}{3}}$. $\ln e^{\frac{1}{3}}$ is in the form $\ln e^x$, and $\ln e^x = x$, thus $\ln e^{\frac{1}{3}} = \frac{1}{3}$. This is because $\ln e^x$ can be rewritten as $\log_e e^x$, and $e$ must be raised to the power of $x$ to become $e^x$.
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