>>854
x^2 > 2^x
log(x^2) > log(2^x)
2 log(x) > x log(2)
(1/x) log(x) > (1/2) log(2)
を示せばいい

f(x) = (1/x) log(x)として
f'(x) = (1-log(x))/x^2

0 < x < e で狭義単調増加
x = e で極大値f(e) = 1/e
x > e で狭義単調減少
f(2) = f(4) = (1/2) log(2)