Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 25

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $\ln \sqrt [ 3 ] { e x }$

• A) \(\frac { 1 } { 3 } + \ln x\)
• B) \(\frac { 1 } { 3 } \ln \mathrm { e } + \frac { 1 } { 3 } \ln \mathrm { x }\)
• C) \(\frac { 1 } { 3 } + \frac { 1 } { 3 } \ln x\)
• D) \(\frac { 1 } { 3 } \ln ( e x )\)

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Definitions:

Competitive Industry

An industry in which no single firm has the power to influence the price of its product; there are many sellers and buyers, and products are largely homogeneous.

Limited Supply

A condition where the availability of a particular good is restricted in the market, often leading to increased prices.

Production Efficiency

A state in which the economy or a production process can no longer produce additional amounts of a good without lowering the production level of another product.

Long-Run Equilibrium

A state in which all factors of production can be adjusted, market supply equals demand, and economic agents have no incentive to change their behavior, leading to a steady-state market condition.