Answer
$ log_{4}5-log_{4}9-log_{4}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, $log_{4}\frac{5}{9z}=log_{4}5-log_{4}9z$.
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_{4}5-(log_{4}9z)= log_{4}5-(log_{4}9+log_{4}z)= log_{4}5-log_{4}9-log_{4}z $.
