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-Earnings Ratio

A financial ratio that measures a company's current share price relative to its per-share earnings.

Total Debt Ratio

A measure of a company's financial leverage, calculated by dividing its total liabilities by its total assets.

Current Ratio

A financial metric indicating how capable a company is of meeting its short-term liabilities using its available assets.

Current Assets

Assets that are expected to be converted into cash, sold, or consumed within one year or within the business's normal operating cycle.