Expand into Sums And/or Differences of Logarithms $\log _ { 1 / 2 } ( a b c )$

question 42

Multiple Choice

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log _ { 1 / 2 } ( a b c )$

• A) \(\frac { 1 } { 2 } \log a + \frac { 1 } { 2 } \log b + \frac { 1 } { 2 } \log c\)
• B) \(\left( \log _ { 1 / 2 } a \right) \left( \log _ { 1 / 2 } b \right) \left( \log _ { 1 / 2 } c \right)\)
• C) \(\log _ { 1 / 2 } a - \log _ { 1 / 2 } b - \log _ { 1 / 2 } c\)
• D) \(\log _ { 1 / 2 } a + \log _ { 1 / 2 } b + \log _ { 1 / 2 } c\)

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Definitions:

Solids

Materials with a fixed shape and volume, characterized by strong intermolecular forces.

Density

A physical property defined as the mass per unit volume of a substance, often used to identify or characterize materials.

Volume

The amount of space that an object or substance occupies, measured in cubic units.

Mass

An assessment of how much matter an object holds, often measured in grams or kilograms.