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: 13

Answer

$x=4$

Work Step by Step

We are given the exponential equation $3^{1-x}=\frac{1}{27}$. We can express each side using a common base and then solve for $x$. $3^{1-x}=3^{-3}=\frac{1}{3^{3}}\frac{1}{27}$ Take the natural log of both sides. $ln(3^{1-x})=ln(3^{-3})$ $(1-x)ln(3)=-3ln(3)$ Divide both sides by $ln(3)$. $1-x=-3$ Subtract 1 from both sides. $-x=-4$ Divide both sides by -1. $x=4$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.