Answer
$x=2$
Work Step by Step
Since $\log_b y=x$ implies $b^x=y,$ the given equation, $
\log_4 x=\dfrac{1}{2}
,$ is equivalent to
\begin{align*}
4^{\frac{1}{2}}&=x
.\end{align*}
Since $x^{\frac{m}{n}}$ is equivalent to $\sqrt[n]{x^m},$ the equation above is equivalent to
\begin{align*}
\sqrt[2]{4^1}&=x
\\
\sqrt[]{4}&=x
\\
2&=x
.\end{align*}
Hence, the solution to the equation $\log_4 x=\dfrac{1}{2}$ is $x=2$.
