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) \(\frac { 1 } { 2 } \ln x\)

---

Definitions:

Operating Costs

Operating costs are expenses associated with the maintenance and administration of a business on a day-to-day basis.

Depreciation Expense

The allocated portion of the cost of a fixed asset, written off each year over the asset's useful life for accounting and tax purposes.

Scarcity

Occurs when the amount people desire exceeds the amount available at a zero price.

Choice

The act of selecting between two or more possibilities, often present in decision-making processes.