Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Sections 9.1-9.6 - Integrated Review - Functions and Properties of Logarithms: 21

Answer

$x=7$

Work Step by Step

We are given that $9=3^{x-5}$. Both of these numbers are powers of 3, so we can rewrite the equation as $3^{2}=3^{x-5}$. 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, $2=x-5$. To solve for x, add 5 to both sides. $x=7$
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