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 - Page 404: 40


$x=\ln 3\approx 1.0986$

Work Step by Step

We need to solve: $e^{2x}-e^{x}-6=0$ We factor: $(e^{x}-3)(e^{x}+2)=0$ $e^{x}+2=0$ or $e^{x}-3=0$ $e^x=-2$ or $e^x=3$ $x=\ln(-2)=$ no solution or $x=\ln 3\approx 1.0986$ (The left equation has no solution because we can't take a log of a negative number.)
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