Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 136

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
- $\log \frac { 6 x ^ { 5 } \sqrt [ 3 ] { 2 - x } } { 5 ( x + 2 ) ^ { 2 } }$

• A) \(\log 6 + \log x ^ { 5 } + \log ( 2 - x ) ^ { 1 / 3 } - \log 5 - \log ( x + 2 ) ^ { 2 }\)
• B) \(\log \left( 6 x ^ { 5 } \sqrt [ 3 ] { 2 - x } \right) - \log \left( 5 ( x + 2 ) ^ { 2 } \right)\)
• C) \(\log 6 + 5 \log x + \frac { 1 } { 3 } \log ( 2 - x ) - \log 5 + 2 \log ( x + 2 )\)
• D) \(\log 6 + 5 \log x + \frac { 1 } { 3 } \log ( 2 - x ) - \log 5 - 2 \log ( x + 2 )\)

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Definitions:

Nonsystematic Risk

The risk associated with an individual investment or a small group of investments, which can be mitigated through diversification.

Treynor-Black Model

An optimization tool used by portfolio managers to balance the trade-off between risk and return by combining actively selected securities with a passively managed market portfolio.

Nonsystematic Risk

The risk associated with a specific issuer of a security, industry, or sector, which can be mitigated through diversification.

Systematic Risk

The risk inherent to the entire market or entire market segment, which cannot be mitigated through diversification.