Answer
$log_{6}5+log_{6}y-2log_{6}z$
Work Step by Step
The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{6}\frac{5y}{z^{2}}=log_{6}5y-log_{6}z^{2}$.
The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $ log_{6}5y-log_{6}z^{2}= log_{6}5+log_{6}y-log_{6}z^{2}$.
The power property of logarithms tells us that $log_{b}x^{r}=r log_{b}x$ (where x and b are positive real numbers, $b\ne1$, and r is a real number).
Therefore, $ log_{6}5+log_{6}y-log_{6}z^{2}= log_{6}5+log_{6}y-2log_{6}z$.
