Use the Properties of Logarithms to Expand $\ln \sqrt [ 5 ] { \frac { x ^ { 2 } } { x + 3 } }$

question 100

Multiple Choice

Use the properties of logarithms to expand $\ln \sqrt [ 5 ] { \frac { x ^ { 2 } } { x + 3 } }$ .

• A) \(( \ln x ) ^ { 2 / 5 } - \ln x \cdot \ln 3\)
• B) \(- 5 ( 2 \ln x - \ln ( x + 3 ) )\)
• C) \(\frac { 1 } { 5 } ( 2 \ln x - \ln x \cdot \ln 3 )\)
• D) \(\frac { 2 } { 5 } \ln x - \frac { 1 } { 5 } \ln ( x + 3 )\)
• E) \(\left( \frac { ( \ln x ) ^ { 2 } } { \ln x + \ln 3 } \right) ^ { 1 / 5 }\)

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Definitions:

Disposable Income

The liquidity households have for spending and saving, after income taxes have been deducted.

Consumption

The act of using goods and services by households that leads to a decrease in their availability.

APC

In economics, stands for Average Propensity to Consume, which is the ratio of total consumption to total disposable income.

APC

Average Propensity to Consume, which is the fraction of income that households spend on consumption as opposed to saving.