Rewrite the Expression as the Sum And/or Difference of Logarithms $\log _ { 17 } \sqrt { \frac { \mathrm { mn } } { 8 } }$

Multiple Choice

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible.
- $\log _ { 17 } \sqrt { \frac { \mathrm { mn } } { 8 } }$

A) $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} + \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } - \log _ { 17 } 8$
B) $\frac { 1 } { 2 } \log _ { 17 } \mathrm { mn } - \frac { 1 } { 2 } \log _ { 17 } 8$
C) $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} + \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } - \frac { 1 } { 2 } \log _ { 17 } 8$
D) $\frac { 1 } { 2 } \log _ { 17 } \mathrm {~m} \cdot \frac { 1 } { 2 } \log _ { 17 } \mathrm { n } \div \frac { 1 } { 2 } \log _ { 17 } 8$