Use the Properties of Logarithms to Expand the Expression as a Sum

question 39

Multiple Choice

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)
$$\ln \frac { x } { \sqrt [ 3 ] { x ^ { 5 } - 2 } }$$

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

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Definitions:

Income Elasticity

The percentage change in the quantity of a product demanded divided by the percentage change in consumer income that caused the change in quantity demanded. It measures the responsiveness of the demand for a good to a consumer’s change in income.

Perfectly Elastic

Describes a situation where the quantity demanded or supplied reacts extremely to a small change in price, indicating infinite responsiveness.

Demand Curve

A graph representing the relationship between the price of a good or service and the quantity demanded by consumers at those prices.

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in its price, indicating the sensitivity of consumers to price changes.