I wouldn't say that logic and religion are totally separate, they are both interconnected. Our logic affects whether we believe in religion and allows us to form our opinions of religion.
What mijy said about the toaster in space is very true to a point, thats why I believe in the possibility of a God or "higher power", whether it created the big bang or not.
I believe that there would be intelligent life somewhere else out there in the universe, because the way I see it, the size of the universe is said to be infinite, so there must be an infinite number of possibilities of what is out there in the universe, therefore, there must be intelligent life somewhere else out there in the universe. I don't know if I'm making any sense, but meh, it makes sense to me lol.