Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set: 12

Answer

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

Work Step by Step

RECALL: (i) If $a^M=a^N$, then $M=N.$ (ii) $(a^m)^n=a^{mn}.$ Write 125 and 625 as powers of 5: $125^{x}=625 \\(5^3)^x=5^4.$ Use rule (ii) above to obtain $5^{3x}=5^4.$ Use rule (i) above to obtain $3x=4 \\x=\frac{4}{3}.$
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