Algebra: A Combined Approach (4th Edition)

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

Chapter 12 - Section 12.6 - Integrated Review - Functions and Properties of Logarithms: 23

Answer

$x=3$

Work Step by Step

$25^{x}=125^{x-1}$ Rewrite $25$ as $5^{2}$ and $125$ as $5^{3}$: $(5^{2})^{x}=(5^{3})^{x-1}$ Multiply the exponents on both sides of the equation: $5^{2x}=5^{3x-3}$ If $5^{2x}=5^{3x-3}$, then $2x=3x-3$: $2x=3x-3$ Solve for $x$: $2x-3x=-3$ $-x=-3$ $x=3$
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