This question already has an answer here:
N[Log[10, 6613], 20] give the requested 20 digits of precision
(* $3.8203985227039816648$ *)
N[Log[10, 6613.3], 20] does not?
(* $3.82042$ *)
The documentation for
"The precision of the output tracks the precision of the input" so one might expect more digits in the output for the latter case.