Expand the Logarithmic Expression $\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)$

question 97

Multiple Choice

Expand the logarithmic expression. $\ln \left( x \sqrt { x ^ { 2 } + 1 } \right)$

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

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Definitions:

Price Increases

A rise in the cost of goods or services, often measured by the rate of inflation.

Quantity Demanded

The total amount of a good that consumers are willing to purchase at a given price over a specified period.

Monopolistically Competitive Firm

A company that operates in a market with many competitors, each offering slightly differentiated products.

Product Differentiation

Making a product or service stand out to a particular target market by distinguishing it from competitors.