Answer
$x=49$
Work Step by Step
Converting to exponential form, the solution to the given logarithmic equation, $
\log_x{7}=\dfrac{1}{2}
,$ is:
\begin{array}{l}\require{cancel}
x^{1/2}=7
\\\\
\sqrt{x}=7
\\\\
\left( \sqrt{x} \right)^2=(7)^2
\\\\
x=49
.\end{array}