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

question 21

Multiple Choice

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) \(\frac { 1 } { 5 } \log b x + \frac { 1 } { 2 } \log b y - 8 \log b z\)

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Definitions:

Cowper's Glands

Small glands located on either side of the urethra in males that secrete a pre-ejaculate fluid contributing to lubrication and neutralizing acidity in the urethra.

Mucus

A slippery secretion produced by mucous membranes, serving to moisten and protect them.

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The process of releasing semen from the penis during sexual arousal or orgasm.

Fallopian Tubes

Tubes through which eggs travel from the ovaries to the uterus in the female reproductive system.