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

question 57

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

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Definitions:

Expression

A combination of symbols, numbers, and operations (such as addition and multiplication) that represents a mathematical concept.

Factor

One of two or more expressions that are multiplied together to form a product or an element that divides another number or expression without leaving a remainder.

Factor

A number or algebraic expression that divides another number or expression evenly—without leaving a remainder.

Trinomial

A polynomial with three terms.