Combine into a Single Logarithm $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

question 7

Multiple Choice

Combine into a single logarithm. $\log ( x - 3 ) + \log ( x + 3 ) - \frac { 1 } { 2 } \log \left( x ^ { 2 } + 9 \right)$

• A) \(\log \left( \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 } \right)\)
• B) \(\log \left( \frac { \sqrt { x ^ { 2 } - 9 } } { x ^ { 2 } } + 9 \right)\)
• C) \(\log \left( \frac { x ^ { 2 } - 9 } { \sqrt { x ^ { 2 } + 9 } } \right)\)
• D) \(\log \left( \frac { x - 3 } { x + 3 } \right)\)
• E) \(\log \left( \frac { x - 9 } { \sqrt { x + 9 } } \right)\)

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Definitions:

Risk-free Rate

The theoretical rate of return on an investment with zero risk, often represented by government bonds.

Risk Premium

The extra return above the risk-free rate that investors demand for choosing to invest in a riskier asset.

Well-diversified Portfolio

An investment portfolio strategically crafted to include a variety of asset classes in order to minimize risk.

Regression Coefficient

A quantitative measure in statistics that represents the strength and direction of the relationship between a dependent variable and an independent variable in a regression analysis.