Is Athiesm really concluded by logic or is it experiencing the world that leads to lack of faith in a God?

Atheists spout that logic is what makes their beliefs so valid but I find this to be specious reasoning. I don't doubt that Atheists are the "logic/factual" type. But didn't Descartes boil reality down to "I think, therefor I am"? So, is it really a point of logic that there can be no god? If this is so then explain it using the aforementioned logic please.