Understanding when to use approximation is very important in this kind of calculation. Wolfram probably knows when an approximation will give the same answer, and uses that. log(2^82589933 - 1)/log(919) - log(2^82589933)/log(919) gives 0 in Wolfram Alpha. Wolfram gives the same answer as we get in Clojure, only with more digits:
(* (Math/log 2) 82589933 (/ (Math/log 919)))
;= 8389942.642742455
I’m sure you can calculate the accuracy of the approximation if you need to. It’s probably accurate to far more than 100 digits.