I am feeling a bit slow today. In Analytic Number Theory it is usual to express asymptotic bounds by specifying the relation of the constant to a specific variable, i.e.
$\log n \ll_\epsilon n^\epsilon$
which means that $\log n \leqslant C_\epsilon n^\epsilon$ for sufficiently large $n$, where the constant $C_\epsilon$ depends only on the constant $\epsilon$.
Could someone explain what are the benefits of this versus just using the usual $\ll$.
I understand that $f \ll_\epsilon g \Rightarrow f \ll g$? Is it equivalent or is it a stronger statement?