Express the Following as a Single Logarithm $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

Multiple Choice

Express the following as a single logarithm. (Assume that all variables represent positive real numbers.) $3 \log b x + \frac { 1 } { 2 } \log _ { b } ( x - 2 ) - 7 \log b ( 3 x + 8 )$

A) $\log b \left( \frac { x ^ { 3 } \sqrt { x - 2 } } { ( 3 x + 8 ) ^ { 7 } } \right)$
B) $\log b \left( \frac { ( x - 2 ) ^ { 7 } \sqrt { x } } { ( 3 x + 8 ) ^ { 3 } } \right)$
C) $\log b \left( \frac { x ^ { 7 } } { \sqrt { x - 2 } ( 3 x + 8 ) ^ { 3 } } \right)$
D) $\log b \left( \frac { x ^ { 7 } } { \sqrt { 3 x + 8 } ( x - 2 ) ^ { 3 } } \right)$