Use the Properties of Logarithms to Rewrite the Expression $\log _ { 5 } \left( \frac { 8 \sqrt { m } } { n } \right)$

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log _ { 5 } \left( \frac { 8 \sqrt { m } } { n } \right)$

A) $\log _ { 5 } 8 + \frac { 1 } { 2 } \log _ { 5 } m - \log _ { 5 } n$
B) $\log _ { 5 } 8 \cdot \left( \frac { 1 } { 2 } \log _ { 5 } m \right) \div \log _ { 5 } n$
C) $\log _ { 5 } n - \log _ { 5 } 8 - \frac { 1 } { 2 } \log _ { 5 } m$
D) $\log _ { 5 } 8 + \sqrt { \log _ { 5 } m } - \log _ { 5 } n$