Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set: 12

Answer

$x=\frac{4}{3}$

Work Step by Step

Note that: $125=5^3$ AND $625=5^4$ Write each side with a base of $5$ to obtain: $(5^3)^{x}=5^4 \\5^{3x}=5^4$ RECALL: If $a^x = a^y$, then $x=y$. Use the rule above to obtain: $5^{3x}=5^4 \\3x=4 \\x=\frac{4}{3}$
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