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: 22

Answer

$x=-\frac{4}{3}$

Work Step by Step

We are given the exponential equation $e^{x+4}=\frac{1}{e^{2x}}$. We can express each side using a common base and then solve for $x$. $e^{x+4}=e^{-2x}=e^{-(2x)}=\frac{1}{e^{2x}}$ Take the natural log of both sides. $ln(e^{x+4})=ln(e^{-2x})$ $(x+4)ln(e)=-2xln(e)$ Divide both sides by $ln(e)$. $x+4=-2x$ Subtract $x$ from both sides. $4=-3x$ Divide both sides by -3. $x=-\frac{4}{3}$
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