College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.5 - Exponential and Logarithmic Equations - 4.5 Exercises - Page 446: 31

Answer

$x=\ln\frac{3}{2}$

Work Step by Step

Let $u=e^x$ $2e^{2x}+e^x-6=0$ $2u^2+u-6=0$ Factor. $(2u-3)(u+2)=0$ Equate each factor to 0. $u=\frac{3}{2}$ or $u=-2$ Since $e^x\gt0$ for all values of $x$ Choose only: $u=\frac{3}{2}=e^x$ Take the natural log of both sides. $x=\ln\frac{3}{2}$
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