Answer
$log_{5}2$
Work Step by Step
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, $log_{5}14+log_{5}3-log_{5}21= log_{5}(14\times3)-log_{5}21= log_{5}42-log_{5}21$.
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_{5}42-log_{5}21=log_{5}\frac{42}{21}=log_{5}2$
