How do you find an asymptotic relation to a given type of function. I was reading a paper by P. Sebah and X. Gourdon , and in that paper they gave the asymptotic relation

$\displaystyle \ln (\zeta (sn))\sim \frac{1}{2^{sn}}$

also it is mentioned that to get 20 digits, only

$\displaystyle \frac{20}{\log_{10}(4)}\approx 33$

are required. I didn't know how get these results. Can someone help me?