Intermediate Algebra (6th Edition)

Published by Pearson

Chapter 9 - Review: 32

Answer

$x=-2$

Work Step by Step

We are given that $3^{x}=\frac{1}{9}$. Both of these numbers are powers of 3, so we can rewrite the equation as $3^{x}=3^{-2}$. We know that $3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}$. From the uniqueness of $b^{x}$, we know that $b^{x}=b^{y}$ is equivalent to $x=y$ (when $b\gt0$ and $b\ne1$). Therefore, $x=-2$.

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.