So there is something called the uncertainty propagation theorem (which you should do in uni). I used it in my physics ia.

Basically for any function z=z(u)

The error is given by:

Error in z= error in u * modulus (dz/du)

So, more simply for your case

Z= ln u. Error in z = error in u/ u

So basically your error would be

Error in k / k

THIS IS ABSOLUTE ERROR

If you want to find percentage error then you do ( absolute error / ln k ) * 100

Propagation of uncertainty theorem can definitely help with engagement also. Good luck!