Intermediate Algebra (6th Edition)

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

Chapter 9 - Section 9.3 - Exponential Functions - Exercise Set: 34

Answer

$x=\frac{8}{3}$

Work Step by Step

We are given that $125^{x-2}=25$. Both of these numbers are powers of 5, so we can rewrite the equation as $(5^{3})^{x-2}=5^{3x-6}=5^{2}$. 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, $3x-6=2$. Add 6 to both sides. $3x=8$ Divide both sides by 3. $x=\frac{8}{3}$
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