Expand the Logarithmic Expression $\log _ { 6 } \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)$

question 108

Multiple Choice

Expand the logarithmic expression. $\log _ { 6 } \left( \frac { 4 x ^ { 3 } } { \sqrt { y } ( x - 2 ) ^ { 6 } } \right)$

• A) \(3 \log _ { 6 } 2 + 2 \log _ { 6 } x - \frac { 1 } { 2 } \log _ { 6 } y - 6 \log _ { 6 } ( x - 2 )\)
• B) \(\log _ { 6 } 2 + 3 \log _ { 6 } x - 2 \log _ { 6 } y - 6 \log _ { 6 } ( x - 2 )\)
• C) \(2 \log _ { 6 } 2 + 3 \log _ { 6 } x - \frac { 1 } { 2 } \log _ { 6 } y + 6 \log _ { 6 } ( x - 2 )\)
• D) \(2 \log _ { 6 } 2 - 3 \log _ { 6 } x - \log _ { 6 } y - \frac { 1 } { 2 } \log _ { 6 } ( x - 6 )\)
• E) none

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Definitions:

Proximodistal Trend

The pattern of development in which growth starts at the center of the body and moves towards the extremities.

Physical Development

The biological growth and maturation process in humans, including motor skills development and changes in body size and strength.

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The parts of the human body at the end of the arms, consisting of the palm and digits, used for grasping and manipulating objects.

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Parts of the human body where the shoulders are the joints connecting the upper arms to the torso, facilitating arm movement.