Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
-$\log _ { 4 } \sqrt { 11 x }$
A) $\frac { 1 } { 2 } \log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$
B) $\log _ { 4 } \sqrt { 11 } + \log _ { 4 } \sqrt { x }$
C) $\log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$
D) $\frac { 1 } { 2 } \log _ { 4 } 11 x$

Question

Quizplus · Accepted Answer

The expression $\log _ { 4 } \sqrt { 11 x }$ can be rewritten using the properties of logarithms. The square root can be expressed as a power of $\frac{1}{2}$, leading to $\log _ { 4 } (11x)^{\frac{1}{2}}$, which can then be expanded using the power rule of logarithms as $\frac { 1 } { 2 } \log _ { 4 } 11 + \frac { 1 } { 2 } \log _ { 4 } x$.

Use Properties of Logarithms to Expand the Logarithmic Expression as Much