Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.5 Logarithmic Functions - 2.5 Exercises - Page 98: 31


$\displaystyle \ln 3+\frac{1}{2}\ln 5-\frac{1}{3}\ln 6$

Work Step by Step

...Apply rule: $\displaystyle \log_{a}\frac{x}{y}=\log_{a}x-\log_{a}y$ $\displaystyle \ln\frac{3\sqrt{5}}{\sqrt{3}{6}}=$ $=\ln(3\cdot\sqrt{5})-\ln(\sqrt[3]{6})$ ... Apply rule: $\log_{a}xy=\log_{a}x+\log_{a}y$ $=\ln 3+\ln\sqrt{5} \ln(\sqrt[3]{6})$ ... $\sqrt[3]{6}=6^{1/3}, \sqrt{5}=5^{1/2}$ $=\ln 3+\ln 5^{1/2}-\ln 6^{1/3}$ ... Apply rule: $ \log_{a}x^{r}=r\log_{a}x$ $=\displaystyle \ln 3+\frac{1}{2}\ln 5-\frac{1}{3}\ln 6$
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