Write the Logarithm as a Sum or Difference of Logarithms $$\log _ { 5 } \left[ \frac { 125 a ^ { 5 } \sqrt { 8 - b } } { c ( b + 7 ) ^ { 2 } } \right]$$

Multiple Choice

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible.
- $$\log _ { 5 } \left[ \frac { 125 a ^ { 5 } \sqrt { 8 - b } } { c ( b + 7 ) ^ { 2 } } \right]$$

A) $3 + 5 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } ( 8 - b ) - \log _ { 5 } c - 2 \log _ { 5 } ( b + 7 )$
B) $15 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } 8 + \frac { 1 } { 2 } \log _ { 5 } b + \log _ { 5 } \mathrm { c } + 2 \log _ { 5 } b + 2 \log _ { 5 } 7$
C) $3 + 5 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } 8 - \frac { 1 } { 2 } \log _ { 5 } b - \log _ { 5 } \mathrm { c } - 2 \log _ { 5 } b - 2 \log _ { 5 } 7$
D) $15 \log _ { 5 } a + \frac { 1 } { 2 } \log _ { 5 } ( 8 - b ) - \log _ { 5 } c - 2 \log _ { 5 } ( b + 7 )$