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: 8

Answer

-0.725

Work Step by Step

We are given the equation $6^{-x+1}=22$. In order to solve, we must first take the natural log of both sides. $ln(6^{-x+1})=ln(22)$ $(-x+1)ln(6)=ln(22)$ Divide both sides by $ln(6)$. $-x+1=\frac{ln(22)}{ln(6)}$ Subtract 1 from both sides. $-x=\frac{ln(22)}{ln(6)}-1$ Multiply both sides by -1. $-x=-\frac{ln(22)}{ln(6)}+1\approx-0.725$
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