It's easy to determine how many digits you'll have in the resulting number.

I'm a bit puzzled: sure, logarithms let you replace multiplication with addition -- part of the magic of slide rules -- but isn't taking the base-10 log of something typically as much or more labor intensive then doing the multiplication?

For example: 321 * 311 produces five digits, while 321 * 312 produces six digits.

Sure, you could work out that 10 ** 2.5065 * 10 ** 2.493 = 10 ** 4.9995 and thus five digits, while 10 ** 2.5065 * 10 ** 2.494 = 10 ** 5.0005 and thus six, but is that really easier?