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

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

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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}

User Cfedermann
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