math.log10 works perfectly on integers which are too large to be converted to floats. I see no reason why it couldn't work as well with fractions.

>>> math.log10(math.factorial(10000))
35659.45427452078
>>> math.log10(math.factorial(1000000))
5565708.917186718
>>> math.log10(float(math.factorial(10000)))
Traceback (most recent call last):
  File "<pyshell#36>", line 1, in <module>
    math.log10(float(math.factorial(10000)))
OverflowError: int too large to convert to float