College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.4 - Laws of Logarithms - 4.4 Exercises: 71

Answer

$\ln(x+\sqrt{x^{2}-1})$

Work Step by Step

$-\ln(x-\sqrt{x^{2}-1})=\ln(x-\sqrt{x^{2}-1})^{-1}=\ln(\frac{1}{x-\sqrt{x^{2}-1}})=\ln(\frac{1}{x-\sqrt{x^{2}-1}}*\frac{x+\sqrt{x^{2}-1}}{x+\sqrt{x^{2}-1}})=\ln(\frac{x+\sqrt{x^{2}-1}}{x^{2}-(x^{2}-1)})=\ln(\frac{x+\sqrt{x^{2}-1}}{1})=\ln(x+\sqrt{x^{2}-1})$
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