What is it you are stuck on?

You need to prove that it is a homomorphism, and that it is a bijection.

Homomorphism is relatively easy to prove - logs take multiplication and make them into addition which is precicely what you are wanting to do here (your first R is under multiplication, you second is under addition).

To show it is an isomorphism it is easiest to find the inverse of log (why are these now equivalent?). So...what is the inverse of taking logs?