I haven't done any of that stuff in a long time so I don't really remember but I'll take a stab at this. From what I remember, a logarithm is just an exponent or it's a way to solve for an exponent. I mean, that's one way of looking at it. An example would work best here I guess:
10^x = 100 can be rewritten as log10(100)=x
Basically, to find the logarithm, just ask yourself how many times you have to multiply 10 by itself to make it equal to 100. It'd be 2 in this case but this was a simple example and it gets more complicated than this. I'm sure there are formulas you can use to help you do logarithms by hand but I don't remember them off the top of my head.
I think I'm remembering this right. Idk exactly what you were looking for Pariah or if this helped, but that's my two cents on the subject.