College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 4 - Section 4.2 - Exponential Functions - 4.2 Exercises: 62

Answer

$x=\frac{1}{3}$

Work Step by Step

We rewrite the 125 on the left, so that the base is 5 on both sides. Left side: $125^x=(5^3)^x$. By the law of exponents: $(5^3)^x=5^{3x}$ Right side: $5=5^1$ Since both sides have the same base of $5$, they will only be equal if their exponents are also equal. Equate the exponents to obtain: $3x=1$ $x=\frac{1}{3}$
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