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: 63


$-2\ln \left( x-1\right) $

Work Step by Step

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