Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 61

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $$\log \left[ \frac { 8 x ^ { 4 } \sqrt [ 4 ] { 5 - x } } { 3 ( x + 5 ) ^ { 2 } } \right]$$

• A) \(\log 8 + 4 \log x + \frac { 1 } { 4 } \log ( 5 - x ) - \log 3 - 2 \log ( x + 5 )\)
• B) \(\log 8 + \log x ^ { 4 } + \log ( 5 - x ) ^ { 1 / 4 } - \log 3 - \log ( x + 5 ) ^ { 2 }\)
• C) \(\log \left( 8 x ^ { 4 } \sqrt [ 4 ] { 5 - x } \right) - \log \left( 3 ( x + 5 ) ^ { 2 } \right)\)
• D) \(\log 8 + 4 \log x + \frac { 1 } { 4 } \log ( 5 - x ) - \log 3 + 2 \log ( x + 5 )\)

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Definitions:

Prn Dose

A prn dose, short for "pro re nata," is a medication prescribed to be taken "as needed" rather than on a regular, fixed schedule, typically used for symptoms that occur intermittently or vary in intensity.

Antipsychotic Drug

A class of medication primarily used to manage psychosis, including disorders such as schizophrenia, by modulating neurotransmitter activity in the brain.

Voluntarily Hospitalized

The act of admitting oneself to a hospital or mental health facility without coercion, often for treatment of a psychiatric condition.