Use the Properties of Logarithms to Rewrite the Expression $\log b \sqrt { \frac { 4 x ^ { 3 } } { z ^ { 8 } } }$

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log b \sqrt { \frac { 4 x ^ { 3 } } { z ^ { 8 } } }$

A) $\log _ { b } 2 \cdot \frac { 3 } { 2 } \log _ { b } x - 4 \log _ { b } z$
B) $\left( \log _ { b } 2 + + \frac { 3 } { 2 } \log _ { b } x \right) \div 4 \log _ { b } z$
C) $\log _ { b } 2 + \frac { 3 } { 2 } \log _ { b } x - 4 \log _ { b } z$
D) $\sqrt{\log _{b} 4}+\sqrt{\log _{b} x^{3}}-\sqrt{\log _{b} z^{8}}$