Question

which is the correct expression for 1 /3 (log x - log y )

Answer 1

As according to rule of logarithm:

$\log (a)-\log (b)=\log (\frac{a}{b})$

And

$a(\log b)=\log (b^a)$

Now applying both rules in given question:

$\begin{gathered} \frac{1}{3}(\log x-\log y)=\frac{1}{3}(\log \frac{x}{y}) \\ \frac{1}{3}(\log \frac{x}{y})=\log (\frac{x}{y})^{\frac{1}{3}} \\ \log (\frac{x}{y})^{\frac{1}{3}}=\log (\sqrt[3]{\frac{x}{y}}) \end{gathered}$