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 ((a)/(b))`

And

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

Now applying both rules in given question:

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