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

question 46

Multiple Choice

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

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

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Definitions:

Long Run

A period of time in economics during which all factors of production and costs are variable, allowing for full industry adjustment.

Diseconomies Of Scale

Situations where a firm's costs per unit increase as the scale of production increases, typically due to inefficiencies that arise from becoming too large.

Diminishing Returns

A principle stating that if one input in the production of a commodity is increased while other inputs are held fixed, a point will eventually be reached at which additions of the input yield progressively smaller, or diminishing, increases in output.

Diminishing Returns

A principle in economics that states as one input variable is incrementally increased, there comes a point when the rate of resultant output begins to decrease.