# "Sub" Logarithmic Equations

• Jul 7th 2008, 01:26 PM
mankvill
"Sub" Logarithmic Equations
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?
• Jul 7th 2008, 01:30 PM
o_O
First off you have to take the log of something, ex.: $\log_{\frac{1}{3}}{\color{blue}56}$

As for inputing different logarithmic bases into your calculator, here's a useful property:
$\log_{{\color{blue}a}}{\color{red}b} = \frac{\log_{c} {\color{red}b}}{\log_{c} \color{blue}a}$ 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 $\ln(x) = \log_{e} (x)$)

Example:
$\log_{2}(19) = \frac{\ln(19)}{\ln(2)} = \frac{\log(19)}{\log(2)}$ (base 10 is implied).
• Jul 7th 2008, 01:31 PM
mankvill
...so what buttons do I push to put in the sub? (Doh)
• Jul 7th 2008, 01:35 PM
o_O
Don't know if you saw my edited post but I posted an example.
• Jul 7th 2008, 01:36 PM
mankvill
Oh, I didn't see that.

I understand now! Thanks a ton. (Rock)