I think this means that while Log grows to infinity, it does that so slowly that it can often be treated as if it were a coefficient. Coefficients are ignored in big O notation, hence the negligibly small comment.

Maybe I'm missing context, but that sounds like O(n) or Ω(n).

t/log(t) is 'closer to' t than it is to sqrt(t) as t heads toward infinity.

e.g:

    4/log2(4) = 4/2 = 2
    sqrt(4) = 2

    2^32/log2(2^32) = 2^32/32 = 2^27
    sqrt(2^32) = 2^16