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: 57


$\ln\sqrt[3] {\frac{yz}{x^2}}=\frac{\ln y}{3}+\frac{\ln z}{3}-\frac{2\ln z}{3}$

Work Step by Step

$\ln\sqrt[3] {\frac{yz}{x^2}}=\ln(\frac{yz}{x^2})^{\frac{1}{3}}={\frac{1}{3}}\ln\frac{yz}{x^2}=\frac{1}{3}(\ln yz-\ln x^2)=\frac{1}{3}(\ln y+\ln z-2\ln x)=\frac{\ln y}{3}+\frac{\ln z}{3}-\frac{2\ln z}{3}$
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