Isomorphisms of Product Groups - How to Prove?

Hi MHF,

This is my first post and it's totally cool to ignore this as I have not contributed in helping anyone else yet, but I'm really in a spot and have no one to ask, and do plan on helping others so help would greatly be appreciated...

The Question I'm having trouble with is:

"Determine whether G is Isomorphic to HxK where

That is, the group of reals defined multiplicatively, the group of plus/minus 1 and the group of reals that are positive

In all honesty, I just have no idea where to start. I have no idea how to prove an isomorphism without a mapping explicitly stated. I'm not looking for the answer, just a nudge in the right direction on how to find the mapping (I literally have no idea and google is very difficult with abstract algebra topics)

thanks so much.