Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.5 Properties of Logarithms - 5.5 Assess Your Understanding - Page 305: 36



Work Step by Step

Recall: (1) $\sqrt[m]{a}=a^{\frac{1}{m}}$ (2) $\log_a {x^n}=n\cdot \log_a {x}$. (3) $\log_a{xy}=\log_a{x} +\log_a{y}$ (4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$ Use rule (1) to obtain $\ln {\sqrt[4] {\frac{2}{3}}}=\ln {\frac{2}{3}}^{\frac{1}{4}}=\dfrac{1}{4}\cdot \ln {\frac{2}{3}}.$ Use rule (4) to obtain $\dfrac{1}{4}\cdot \ln {\frac{2}{3}}=\dfrac{1}{4}\cdot \left(\ln {2}-\ln{3}\right)=\dfrac{1}{4}(a-b)$
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