Answer
The statement, ${{\log }_{a}}\frac{m}{n}={{\log }_{a}}m-{{\log }_{a}}n$ is true.
Work Step by Step
${{\log }_{a}}\frac{m}{n}={{\log }_{a}}m-{{\log }_{a}}n$
The quotient rule for logarithms says that, for any positive numbers M, N and a $\left( a\ne 1 \right)$, ${{\log }_{a}}\frac{M}{N}={{\log }_{a}}M-{{\log }_{a}}N$.
Therefore, ${{\log }_{a}}\frac{m}{n}={{\log }_{a}}m-{{\log }_{a}}n$
