Solve the Problem $\mathrm { u } = \ln \mathrm { a }$

question 30

Multiple Choice

Solve the problem.
-Let $\mathrm { u } = \ln \mathrm { a }$ and $\mathrm { v } = \ln \mathrm { b }$ . Write the following expression in terms of $u$ and $\mathrm { v }$ without using the function $\ln$ .
$\ln \left( b ^ { 4 } \sqrt [ 3 ] { a } \right)$

• A) \(4 \mathrm { v } + \frac { \mathrm { u } } { 3 }\)
• B) \(4 \mathrm { v } + \frac { \mathrm { u } } { 4 }\)
• C) \(4 \mathrm { v } - \frac { \mathrm { u } } { 3 }\)
• D) \(4 \mathrm { v } + 3 \mathrm { u }\)

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Definitions:

Consumer Willingness

The maximum amount a consumer is ready to pay for a good or service, reflecting their valuation of it.

Marginal Revenue

The added revenue obtained from trading an additional unit of a product or service.

Decreasing Cost Industry

An industry where an increase in production leads to a decrease in the average cost of producing each unit, often due to economies of scale.

Marginal Cost

Marginal cost refers to the increase in total cost that arises from producing one additional unit of a good or service.