College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding: 54

Answer

$=\dfrac {2}{3}\left( 2\ln \left( x-4\right) -\ln \left( x^{2}-1\right) \right) $

Work Step by Step

We use the rules of logarithms to obtain: $\ln \left[ \dfrac {\left( x-4\right) ^{2}}{x^{2}-1}\right] ^{2/3}=\dfrac {2}{3}\ln \dfrac {\left( x-4\right) ^{2}}{x^{2}-1}=\dfrac {2}{3}\left( \ln \left( x-4\right) ^{2}-\ln \left( x^{2}-1\right) \right) =\dfrac {2}{3}\left( 2\ln \left( x-4\right) -\ln \left( x^{2}-1\right) \right) $
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