Use the Properties of Logarithms to Rewrite the Expression $$\log _ { 19 } \left( \frac { 10 \sqrt { m } } { n } \right)$$

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent
positive real numbers.
- $$\log _ { 19 } \left( \frac { 10 \sqrt { m } } { n } \right)$$

A) $\log _ { 19 } 10 + \frac { 1 } { 2 } \log _ { 19 } m - \log _ { 19 } n$
B) $\log _ { 19 } n - \log _ { 19 } 10 - \frac { 1 } { 2 } \log _ { 19 } m$
C) $\log _ { 19 } 10 + \sqrt { \log _ { 19 } m } - \log _ { 19 } n$
D) $\log _ { 19 } 10 \cdot \left( \frac { 1 } { 2 } \log _ { 19 } m \right) \div \log _ { 19 } n$