I have a calculation using the following pseudo-formula:
$ y = -ln(X/X_o)$
where both $X$ and $X_o$ have an associated error with them. I have propagated the error out simply using:
$ \delta y = y\sqrt{\frac{\delta X}{X} + \frac{\delta X_o}{X_o} } $
However, I'm not sure how to account for the use of the natural log - I feel like this is adequate since my general understanding is that the deviation $S_p$ in a measurement $p$ is found with:
$S_X = \frac{S_p}{p}$
My other thought is to calculate the error as:
$ \delta y = y\sqrt{\ln({\frac{\delta X}{X})} + \ln{(\frac{\delta X_o}{X_o} })} $