$\displaystyle \log_{7}{\left( \frac{x}{y^6} \right)}$\displaystyle \log_{7}{\left( \frac{x}{y^6} \right)}

$\displaystyle \log_{7}{\left(xy\right)^6}$\displaystyle \log_{7}{\left(xy\right)^6}

$\displaystyle \log_{7}{\left(6xy\right)}$\displaystyle \log_{7}{\left(6xy\right)}

$\displaystyle \log_{7}{\left(xy^6\right)}$\displaystyle \log_{7}{\left(xy^6\right)}