Intermediate Algebra (6th Edition)

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

Chapter 11 - Cumulative Review - Page 670: 27a

Answer

$3$

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_5x\\ (\log_5 3)(\log_5 5)=\log_5x\\ (\log_5 3)(1)=\log_5x\\ \log_5 3=\log_5x\\ 3=x &\text{...since the logarithms have the same base} \\ x=3 .\end{array} Hence, $5^{\log_5 3}$ is equal to $ 3 .$
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