Answer
$3$
Work Step by Step
Recall
(1) $\log_a{b}=y \longleftrightarrow a^y=b$
(2) The value of the function $f(x)=\log_a{x}$ increases as $x$ increases.
Let $y=\log_{\sqrt7}{\sqrt{50}}$
Use the definition in (1) above to obtain:
$y=\log_{\sqrt7}{\sqrt{50}}\longrightarrow (\sqrt7)^y=\sqrt{50}$
Note that
$(\sqrt7)^2=7$ while $(\sqrt7)^3=7\sqrt7$
Since $7 \lt \sqrt{50} \lt 7\sqrt7$, then $y$ must be between $2$ and $3$.
Thus, the least integer that is greater than $\log_{\sqrt7}{\sqrt{50}}$ is $3$.
