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".
Any help?
First off you have to take the log of something, ex.: $\displaystyle \log_{\frac{1}{3}}{\color{blue}56}$
As for inputing different logarithmic bases into your calculator, here's a useful property:
$\displaystyle \log_{{\color{blue}a}}{\color{red}b} = \frac{\log_{c} {\color{red}b}}{\log_{c} \color{blue}a}$ 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 $\displaystyle \ln(x) = \log_{e} (x)$)
Example:
$\displaystyle \log_{2}(19) = \frac{\ln(19)}{\ln(2)} = \frac{\log(19)}{\log(2)}$ (base 10 is implied).