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: 61


$\log _{4}\dfrac {\left( x-1\right) }{\left( x+1\right) ^{4}}$

Work Step by Step

We use the rules of logarithms to obtain: $\log _{4}\left( x^{2}-1\right) -5\log _{4}\left( x+1\right) =\log _{4}\left( x^{2}-1\right) -\log _{4}\left( x+1\right) ^{5}=\log _{4}\dfrac {x^{2}-1}{\left( x+1\right) ^5}=\log _{4}\dfrac {\left( x+1\right) \left( x-1\right) }{\left( x+1\right) ^{5}}=\log _{4}\dfrac {\left( x-1\right) }{\left( x+1\right) ^{4}}$
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