Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.3 - Exponential Functions - Exercise Set: 32

Answer

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

Work Step by Step

$125^{x-2}=25$ Rewrite $125$ as $5^{3}$ and $25$ as $5^{2}$: $(5^{3})^{x-2}=5^{2}$ Transform the left side of the equation into a power that has the product of $3$ and $x-2$ as its exponent: $5^{3x-6}=5^{2}$ If $5^{3x-6}=5^{2}$, then $3x-6=2$ $3x-6=2$ Solve for $x$: $3x=2+6$ $3x=8$ $x=\dfrac{8}{3}$
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