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

Multiple Choice

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

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