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 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises: 44

Answer

$x=\ln 5\approx 1.6094$ or $x=\ln 3\approx 1.0986$

Work Step by Step

We need to solve: $e^{x}+15e^{-x}-8=0$ We multiply through by $e^x$ (always positive): $e^x(e^{x}+15e^{-x}-8)=e^x(0)$ $e^{2x}+15-8e^{x}=0$ $(e^{x}-5)(e^{x}-3)=0$ $(e^{x}-5)=0$ or $(e^{x}-3)=0$ $e^x=5$ or $e^x=3$ $x=\ln 5\approx 1.6094$ or $x=\ln 3\approx 1.0986$
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