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: 59


$\ln\sqrt[4] {x^3(x^2+3)}=\frac{3\ln~x}{4}+\frac{\ln(x^2+3)}{4}$

Work Step by Step

$\ln\sqrt[4] {x^3(x^2+3)}=\ln [x^3(x^2+3)]^{\frac{1}{4}}=\frac{1}{4}\ln [x^3(x^2+3)]=\frac{1}{4}[\ln~x^3+\ln(x^2+3)]=\frac{1}{4}[3\ln~x+\ln(x^2+3)]=\frac{3\ln~x}{4}+\frac{\ln(x^2+3)}{4}$
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