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 306: 110


Since $\log_a {x}-\log_a {y}=\log_a {(\frac{x}{y})}$ and $\log_a{1}=0$, then \begin{align*} \log_a{\left(\frac{1}{N}\right)}&=\log_a{1}-\log_a{N}\\ &=0-\log_a{N}\\&=-\log_a{N}\end{align*}

Work Step by Step

We know that $\log_a {x}-\log_a {y}=\log_a {(\frac{x}{y})}$. Hence, $\log_a{\left(\frac{1}{N}\right)}=\log_a{1}-\log_a{N}.$ We also know that $\log_a{1}=0$. Thus, $\log_a{1}-\log_a{N}\\ =0-\log_a{N}\\ =-\log_a{N}$
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