Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.6 - Exponential and Logarithmic Equations; Further Applications - 9.6 Exercises: 7

Answer

0.833

Work Step by Step

We are given the equation $9^{-x+2}=13$. In order to solve, we must first take the natural log of both sides. $ln(9^{-x+2})=ln(13)$ $(-x+2)ln(9)=ln(13)$ Divide both sides by $ln(9)$. $-x+2=\frac{ln(13)}{ln(9)}$ Subtract 2 from both sides. $-x=\frac{ln(13)}{ln(9)}-2$ Multiply both sides by -1. $x=-\frac{ln(13)}{ln(9)}+2\approx0.833$
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