Answer
$ log_{3}\frac{(y^{4}+11y)}{(y+2)}$
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, $log_{3}y-log_{3}(y+2)+log_{3}(y^{3}+11)= log_{3}\frac{y}{(y+2)}+log_{3}(y^{3}+11)$.
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_{3}\frac{y}{(y+2)}+log_{3}(y^{3}+11)= log_{3}(\frac{y}{(y+2)}\times (y^{3}+11))=log_{3}\frac{y(y^{3}+11)}{(y+2)}= log_{3}\frac{(y^{4}+11y)}{(y+2)}$.
