2016/17 AHSMC Part 1 Problem 2

The equation can be written as $(\log_2 x)^2 = \dfrac{1}{2} \log_2 x$, and since $x \neq 1$, this equation is equivalent to $\log_2 x = \dfrac{1}{2}$ with the solution $x = \sqrt{2} \in (1,2)$. The answer is (B).