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: 91

Answer

$x = \frac{1}{2}$

Work Step by Step

RECALL: (1) $a^m \cdot a^n = a^{m+n}$ (2) If $a^m=a^n$, then $m=n$ Use rule (1) above to obtain: $5^{2x+4x}=125 \\5^{6x}=125$ Note that $125=5^3$. Write $125$ as $5^3$ to obtain: $5^{6x} = 5^3$ Use rule (2) above to obtain: $6x=3$ Divide $6$ on both sides of the equation to obtain: $x = \frac{1}{2}$
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