Answer
Use the properties the $\log_a {x}-\log_a {y}=\log_a {(\frac{x}{y})}$ and $\log_a{1}=0$ to obtain:
$f(\frac{1}{x})
\\=\log_a{(\frac{1}{x})}
\\=\log_a{1}-\log_a{x}
\\=0-\log_a{x}
\\=-\log_a{x}
\\=-f(x)$
Work Step by Step
We know that $\log_a {x}-\log_a {y}=\log_a {(\frac{x}{y})}$.
Hence,
$f(\frac{1}{x})=\log_a{(\frac{1}{x})}=\log_a{1}-\log_a{x}.$
We also know that $\log_a{1}=0$.
Thus,
$\log_a{1}-\log_a{x}\\
=0-\log_a{x}\\
=-\log_a{x}\\
=-f(x)$
