2. (2004 High School Mathematics Competition) The solution set of the inequality $\sqrt{\log _{2} x-1}+\frac{1}{2} \log _{\frac{1}{4}} x^{3}+2>0$ is
A. $[2,3)$
B. $(2,3]$
C. $[2,4)$
D. $(2,4]$
2. $C$ Hint: Let $\log _{2} x=t$, the original inequality becomes $\sqrt{t-1}-\frac{3}{2} t+2>0$, solving yields $1 \leqslant t<2$, i.e., $2 \leqslant x<4$.