College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4: 92

Answer

Since $x \ne -1$, there is no solution.

Work Step by Step

$\ln (x-5) - \ln (x+4) = \ln (x-1) - \ln (x+2)$ $\ln \frac{x-5}{x+4} = \ln \frac{x-1}{x+2}$ $ \frac{x-5}{x+4} = \frac{x-1}{x+2}$ $(x-5)(x+2) = (x-1)(x+4)$ $x(x+2)-5(x+2) = x(x+4)-1(x+4)$ $x^{2} + 2x - 5x - 10 = x^{2} + 4x - x - 4$ $x^{2} - 3x - 10 = x^{2} + 3x - 4$ $x^{2} - x^{2} - 3x - 3x - 10 + 4 = 0$ $-6x - 6 = 0 $ $-6x = 6$ $x = -1$ Since $x \ne -1$, there is no solution.
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