x = {Sqrt[2 \[Pi] n] (n/Exp[1])^n, (n/Exp[1])^n, n^n};

test = {4, 90, 10^10};

lsg = Flatten[

Table[FindRoot[(Log[n!] - Log[ x[[i]]])/Log[n!] == 10^-2, {n,

test[[i]]}], {i, 3}]]

Table[Abs[N[(Log[n!] - Log[ x[[i]]])/Log[n!] /. lsg[[i]]]], {i, 3}]

Now I'm using FindRoot, this maybe works. But the third and last value is for different third elements of test differently. Because of the Precision?

Regards,

Niklas Casper