Write the expression as sums or differences of multiples of logarithms.
-$\log _ { 4 } \sqrt { 3 x }$
A) $\frac { 1 } { 2 } \log _ { 4 } 3 \mathrm { x }$
B) $\log _ { 4 } \sqrt { 3 } + \log _ { 4 } \sqrt { x }$
C) $\frac { 1 } { 2 } \log _ { 4 } 3 + \frac { 1 } { 2 } \log _ { 4 } x$
D) $\log _ { 4 } 3 + \frac { 1 } { 2 } \log _ { 4 } \mathrm { x }$

Question

Quizplus · Accepted Answer

The expression $\log _ { 4 } \sqrt { 3 x }$ can be rewritten using the properties of logarithms. The square root can be expressed as a power of $1/2$, and the logarithm of a product can be split into the sum of logarithms. Therefore, $\log _ { 4 } \sqrt { 3 x } = \log _ { 4 } (3x)^{1/2} = \frac { 1 } { 2 } \log _ { 4 } 3 + \frac { 1 } { 2 } \log _ { 4 } x$.

Write the Expression as Sums or Differences of Multiples of Logarithms