branch cuts / complex logs

Hi. So I'm new to branch cuts and I think I get the general idea, but I'm stuck with a couple homework questions along the same lines as:

I'm given the branch cut, eg (x=0, y__>__0)

and told for example log(-1) = -i(pi) on this branch

Then asked to find the value of some other simple complex logs on the same branch

I guess I'm just confused as to how the given value of log(-1) (or log(1) in another question) is relevent... do I need to use it to find a value of k in

log(z)=Log(r) + i(Argz + 2kpi) ?

but then I can't see how I would use the value of k to answer the problem... does the 2kpi even come into it once you have a branch cut? Am I looking at this totally wrong?? v. confused...

sorry if this isn't too coherent, i'm tired.. but any help appreciated! :)