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: 5



Work Step by Step

$\log_a{\frac{M}{N}}=\log_a{MN^{-1}}$. We know that $\log_a {x}+\log_a {y}=\log_a {(x\cdot y)}$. Thus $\log_a{MN^{-1}}=\log_a{M}+\log_a{N^{-1}}$. We know that $\log_a {x^n}=n\cdot \log_a {x}$, hence $\log_a{M}+\log_a{N^{-1}}=\log_a{M}-\log_a{N}$.
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