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: 21

Answer

$x=-2$

Work Step by Step

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