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: 14

Answer

$x=5$

Work Step by Step

We are given the exponential equation $5^{2-x}=\frac{1}{125}$. We can express each side using a common base and then solve for $x$. $5^{2-x}=5^{-3}=\frac{1}{5^{3}}\frac{1}{125}$ Take the natural log of both sides. $ln(5^{2-x})=ln(5^{-3})$ $(2-x)ln(5)=-3ln(5)$ Divide both sides by $ln(5)$. $2-x=-3$ Subtract 2 from both sides. $-x=-5$ Divide both sides by -1. $x=5$
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