# Thread: taking logs

1. ## taking logs

Hi All..

I'm having some trouble trying take logs of this equation below..

$\frac{S_1}{S_2} = \frac{\exp{(-Q/RT_1)}}{\exp{(-Q/RT_2)}}$

From my solution to the answer when I have plugged in the values I get a minus value..when it should be positive. So I think I have not taken the logs properly..

I'm trying to find Q Where all the others are known values.

2. Hi

$\frac{S_1}{S_2} = \frac{e^{-\frac{Q}{RT_1}}}{e^{-\frac{Q}{RT_2}}} = e^{-\frac{Q}{RT_1}}\,e^{\frac{Q}{RT_2}} = e^{Q(\frac{1}{RT_2}-\frac{1}{RT_1})}$

$Q(\frac{1}{RT_2}-\frac{1}{RT_1}) = ln\frac{S_1}{S_2}$

$Q = \frac{1}{\frac{1}{RT_2}-\frac{1}{RT_1}}\,ln\frac{S_1}{S_2}$

3. Thank you for that

yeah I can see where I went wrong.. what happens to the minus sign on the first line before the Q/RT2 ?

4. is there a general rule or does it just cancel out ?

5. $a^{-n}$ is defined to be $\frac{1}{a^n}$

If $u = a^{-1}$, then $u^n$ is defined to be $\frac{1}{u^{-n}}$ and the reverse statement is true.