Giải bất phương trình \({\log _2}\left( {{{\log }_{\frac{1}{2}}}\left( {{2^x} - \frac{{15}}{{16}}} \right)} \right) \le 2\)

A. \(x \ge 0\)

B. \({\log _2}\frac{{15}}{{16}} < x < {\log _2}\frac{{31}}{{16}}\)

C. \(0 \le x < {\log _2}\frac{{31}}{{16}}\)

D. \({\log _2}\frac{{15}}{{16}} < x \le 0\)