CAS: log of large integers?

[Joe Horn]

The HP 50g nicely returns 777 if you do 777 ALOG LOG in exact mode, even though 10^777 is larger than the 50g's MAXREAL. But Prime returns +Inf for log10(10^777), even though 10^777 is an exact integer. Apparently Prime first tries to convert the argument to a real, which in this case immediately overflows.

Question: How can Prime be programmed to return the approximate common log of exact integers which are greater than CAS's MAXREAL? The program should work on any large integer, even square-free integers (even the 50g has trouble with those).