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: 40

Answer

$x=\ln 3\approx 1.0986$

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.)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.