The RHS is a line; the LHS is a concave curve that looks like a logarithm and has x intercept at (2,0).
There are at most two solutions, one of which is 2. But note that at x=2, we have log2log22=0>2−1−2, meaning that the log log curve is above the line, so it must intersect the line again at a point x>2. Now we check x=4 and see that log2log24=1<4−1−2, which means at x=4 the line is already above the loglog curve. Thus, the second solution lies in the interval (2,4). The answer is (D) ≤S<6.