Answer
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,
$\log_a{1}-\log_a{N}\\
=0-\log_a{N}\\
=-\log_a{N}$
