\(\eqalign{
& {\log _{{1 \over 2}}}x + {({\log _2}x)^2} = 2 \cr
& \Leftrightarrow {\log _{{2^{ - 1}}}}x + {({\log _2}x)^2} = 2 \cr
& \Leftrightarrow - {\log _2}x + {({\log _2}x)^2} = 2 \cr
& \Leftrightarrow \left[ \matrix{
{\log _2}x = - 1 \hfill \cr
{\log _2}x = 2 \hfill \cr} \right. \Leftrightarrow \left[ \matrix{
x = {1 \over 2} \hfill \cr
x = 1 \hfill \cr} \right. \cr} \)
