I have a TI-83 Plus and I don't know how to make, say: "log 1/3" where the "1/3" is sub to the "log".
First off you have to take the log of something, ex.:
As for inputing different logarithmic bases into your calculator, here's a useful property:
where c can be any number.
So for your calculator, you'll either be considering c = 10 (denoted just log on the calculator) or c = e (where )
(base 10 is implied).