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: 32


$\displaystyle \ln 9+\frac{1}{3}\ln 5-\frac{1}{4}\ln 3$

Work Step by Step

$\displaystyle \ln\frac{9\cdot\sqrt[3]{5}}{\sqrt[4]{3}}=$ ...Apply rule: $\displaystyle \log_{a}\frac{x}{y}=\log_{a}x-\log_{a}y$ $=\ln(9\cdot\sqrt[3]{5})-\ln(\sqrt[4]{3})$ ...Apply rule: $\log_{a}xy=\log_{a}x+\log_{a}y$ $=\ln 9+\ln\sqrt[3]{5}-\ln(\sqrt[4]{3})$ ... $\sqrt[3]{5}=5^{1/3},\qquad \sqrt[4]{3}=3^{1/4}$ $=\ln 9+\ln 5^{1/3}-\ln 3^{1/4}$ ... Apply rule:$ \log_{a}x^{r}=r\log_{a}x$ $=\displaystyle \ln 9+\frac{1}{3}\ln 5-\frac{1}{4}\ln 3$
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