Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.5 Properties of Logarithms - 5.5 Assess Your Understanding - Page 305: 25



Work Step by Step

We know that $\log_a {x}-\log_a {y}=\log_a {\left(\frac{x}{y}\right)}$. Hence, $3^{\log_3{5}-\log_3 {4}}=3^{\log_3 {\left(\frac{5}{4}\right)}}$. We also know that $a^{\log_a {x}}=x$. Thus, $3^{\log_3 {\left(\frac{5}{4}\right)}}=\frac{5}{4}$.
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