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:

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Standard Deviation

A measure of dispersion or variability that quantifies how much individual data points deviate from the mean of a dataset.

Normally Distributed

Referring to a bell-shaped curve distribution where data are symmetrically distributed around the mean, implying most data points are close to the mean and fewer are near the extremes.

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A rechargeable battery that supplies electrical energy to a motor vehicle, primarily used for starting the engine and powering accessories.