Answer
$log_{6}6$
Work Step by Step
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, $log_{6}21+log_{6}2-log_{6}7=log_{6}(21\times2)-log_{6}7=log_{6}42-log_{6}7$.
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, $log_{6}42-log_{6}7=log_{6}\frac{42}{7}=log_{6}6$.