Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.3 - Properties of Logarithms - 5.3 Exercises - Page 385: 21


$\log_6\sqrt[3] {\frac{1}{6}}=-\frac{1}{3}$

Work Step by Step

Use the Power Property. Also, remeber that $\log_aa=1$: $\log_6\sqrt[3] {\frac{1}{6}}=\log_6\sqrt[3] {6^{-1}}=\log_6(6^{-1})^{\frac{1}{3}}=\log_66^{-\frac{1}{3}}=-\frac{1}{3}\log_66=-\frac{1}{3}(1)=-\frac{1}{3}$
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