Điều kiện: $\left\{\begin{array}{l}x>0\\x\ne1\end{array}\right.$
Bất phương trình đã cho tương đương với:
$\log_4x-\dfrac{2}{\log_4x}<\dfrac{1}{2}$
$\Leftrightarrow \dfrac{\log_4^2x-2}{\log_4x}-\dfrac{1}{2}<0$
$\Leftrightarrow \dfrac{2\log_4^2x-\log_4x-4}{2\log_4x}<0$
$\Leftrightarrow \left[\begin{array}{l}\log_4x<\dfrac{1-\sqrt{33}}{4}\\0<\log_4x<\dfrac{1+\sqrt{33}}{4}\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}0<x<4^\frac{1-\sqrt{33}}{4}\\1<x<4^\frac{1+\sqrt{33}}{4}\end{array}\right.$