Where the scientists/mathematicians at?

Phew, in the middle of a looong planning lab on the discharge of capacitors. 
I need to calculate the error so that I can place error bars on a graph I need to give gradient 1/RC (I'm trying to determine RC time).
Here's the question (my physics teacher told me he would look it up for me but he plainly forgot):
What happens to the error when you take the Natural Logarithm?
I know the standards for BODMAS and root and square functions, but no-one has ever mentioned what it is for logs/natural logs.
That would help me to calculate the correct errors.
Thanks a lot!

I need to calculate the error so that I can place error bars on a graph I need to give gradient 1/RC (I'm trying to determine RC time).
Here's the question (my physics teacher told me he would look it up for me but he plainly forgot):
What happens to the error when you take the Natural Logarithm?
I know the standards for BODMAS and root and square functions, but no-one has ever mentioned what it is for logs/natural logs.

That would help me to calculate the correct errors.
Thanks a lot!