Express $\log b \left( \frac { x ^ { \frac { 1 } { 2 } } y ^ { \frac { 1 } { 5 } } } { z ^ { 8 } } \right)$

Express $\log b \left( \frac { x ^ { \frac { 1 } { 2 } } y ^ { \frac { 1 } { 5 } } } { z ^ { 8 } } \right)$ as the sum or difference of simpler logarithmic quantities. Assume that all variables represent positive real numbers.

A) $\frac { 1 } { 2 } \log b x + \frac { 1 } { 5 } \log b y - 8 \log b z$
B) $\frac { 1 } { 8 } \log _ { b } x - 2 \log _ { b } y + \frac { 1 } { 5 } \log _ { b } z$
C) $8 \log _ { b } z - \frac { 1 } { 2 } \log _ { b } x + \frac { 1 } { 5 } \log b y$
D) $\frac { 1 } { 5 } \log b x + \frac { 1 } { 2 } \log b y - 8 \log b z$

Correct Answer:

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