Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Cumulative Review - Page 670: 27c

Answer

$x=3$

Work Step by Step

Let $5^{\log_5 3}=x$. Taking the logarithm base $5$ of both sides, then, \begin{array}{l} \log_5 5^{\log_5 3}=\log_5 x \\ (\log_5 3)(\log_5 5)=\log_5 x \\ (\log_5 3)(1)=\log_5 x \\ \log_5 3=\log_5 x .\end{array} Since the bases on both sides of the equal sign are the same, then the logarithm base $5$ can be dropped, resulting to $ x=3 .$
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