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 - Page 459: 50


$\dfrac {1}{3}\log _{5}\left( x^{2}+1\right) -\log _{5}\left( x^{2}-1\right) $

Work Step by Step

We use the rules of logarithms to obtain: $\log _{5}\left( \dfrac {\sqrt [3] {x^{2}+1}}{x^{2}-1}\right) =\log _{5} \sqrt [3] {x^{2}+1}-\log \left( x^{2}-1\right) =\log _{5}\left( x^{2}+1\right) ^{\dfrac {1}{3}}-\log _{5}\left( x^{2}-1\right) =\dfrac {1}{3}\log _{5}\left( x^{2}+1\right) -\log _{5}\left( x^{2}-1\right) $
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