Use the Properties of Logarithms to Rewrite the Expression $\log _ { 8 } \left( \frac { 4 \sqrt { 7 } } { 8 } \right)$

question 336

Multiple Choice

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers.
- $\log _ { 8 } \left( \frac { 4 \sqrt { 7 } } { 8 } \right)$
$\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7$

• A) \(\left( \log _ { 8 } 4 \right) \left( \frac { 1 } { 2 } \log _ { 8 } 7 \right) - \log _ { 8 } 8\)
• B) \(\frac { \log 88 } { 2 }\)
• C) \(\log _ { 8 } 4 + \frac { 1 } { 2 } \log _ { 8 } 7 - \log _ { 8 } 8\)
• D) \(\log _ { 8 } 4 + \sqrt { \log _ { 8 } 7 } - \log 88\)

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Definitions:

Sense

A physiological capacity of organisms that provides data for perception, such as sight, sound, smell, taste, touch, and proprioception.

Vision

Vision is the faculty of the eyes to perceive the environment through the light that enters them, allowing humans and other organisms to navigate, identify, and interact with their surroundings.

Hearing

The sensory process by which sound is perceived through the ears and interpreted by the brain.

Smell

A sense involving the detection and identification of molecules in the air, processed by olfactory sensors in the nose.