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 - Page 490: 45



Work Step by Step

Begin by factoring the terms using trial and error. Then set the terms in each set of parentheses equal to $0$ and solve for $x$ by using the natural log on both sides of each equation. $e^{4x}+5e^{2x}-24=0$ $(e^{2x}+8)(e^{2x}-3)=0$ $(e^{2x}+8)=0, (e^{2x}-3)=0$ $e^{2x}=-8, e^{2x}=3$ not possible, $2x=\ln(3)$ $x=\frac{\ln(3)}{2}$ $x\approx0.55$
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