College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.5 - Properties of Logarithms - 6.5 Assess Your Understanding - Page 459: 25

Answer

$\dfrac{5}{4}$

Work Step by Step

Recall: (1) $\log_a{x}-\log_a{y}=\log_a{\left(\frac{x}{y}\right)}$ (2) $a^{\log_a{b}}=b$ Use rule (1) above to obtain: \begin{align*} 3^{\log_3{5}-\log_3{4}}&=3^{\log_3{\left(\frac{5}{4}\right)}} \end{align*} Use rule (2) above to obtain: \begin{align*} 3^{\log_3{\left(\frac{5}{4}\right)}}&=\frac{5}{4} \end{align*}
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