Answer
$log_{4}4$
Work Step by Step
We know 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, $log_{4}2+log_{4}10-log_{4}5=log_{4}2+log_{4}\frac{10}{5}=log_{4}2+log_{4}2$.
We know that $log_{b}xy=log_{b}x+log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$).
Therefore, $log_{4}2+log_{4}2=log_{4}(2\times2)=log_{4}4$.