Use the Properties of Logarithms to Rewrite the Expression $\log \mathrm { b } \left( \frac { m ^ { 5 } p ^ { 2 } } { n ^ { 4 } b ^ { 8 } } \right)$

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log \mathrm { b } \left( \frac { m ^ { 5 } p ^ { 2 } } { n ^ { 4 } b ^ { 8 } } \right)$

A) $5 \log _ { b } m + 2 \log _ { b } p - 4 \log _ { b } n - 8$
B) $m ^ { 5 } p ^ { 2 } - n ^ { 4 } b ^ { 8 }$
C) $5 \log _ { b } m + 2 \log _ { b } p - 4 \log _ { b } n + 8$
D) $\log _ { b } m ^ { 5 } + \log _ { b } p ^ { 2 } + \log _ { b } n ^ { 4 } - \log b b ^ { 8 }$