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) $\log _ { 1 / 2 } a + \log _ { 1 / 2 } b + \log _ { 1 / 2 } c$

Question

Quizplus · Accepted Answer

The properties of logarithms allow for the expansion of $\log _ { 1 / 2 } ( a b c )$ into $\log _ { 1 / 2 } a + \log _ { 1 / 2 } b + \log _ { 1 / 2 } c$, reflecting the multiplication inside the log as a sum of logs.

Expand into Sums And/or Differences of Logarithms log⁡1/2(abc)\log _ { 1 / 2 } ( a b c )log1/2​(abc)

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