log₃(27)=3, so, if log₂(x)=3, x=8, but (log₂(x))²=3²=9, which is not equal to 3, so the question as presented has inconsistencies.
Suppose log₂(x)+log₂(x))²=log₃(27), then (log₂(x))²+log₂(x)-log₃(27)=0, that is:
log₂(x)=(-1±√(1+12))/2=(-1±√13)/2=1.3028 or -2.3028, and x=2^1.3028 or 2^-2.3028=2.467 or 0.2028 approx.
Other answers are possible if another of the equals signs was supposed to be + or -. But two equals signs makes the statement inconsistent and false.