From the dictionary:
"Logic: reason or sound judgment, as in utterances or actions:"
Your quote:
"Logically, what you believe is sound"
Untrue, logically what one believes can quite unsound and not follow a logical path, nor be a result of sound judgement.
By your definition, it was "illogical" to consult the dictionary for the meaning of logic, as that was not sound judgment on your part.
Next time, please consult wikipedia as dictionaries do not always give sound definitions of things:
http://en.wikipedia.org/wiki/Logic
I can't say what the posters original intentions were, but if you ask me "is theism logical" and I believe you are asking me "does theism follow the laws of demonstration, and argumentation formal logic."
The answer is no. Then again, neither does philosophy, history, political science, sociology, mechanical physics, astronomy, biology, chemistry does to some extent but not really. The list goes on, but I won't.
Point is, nobody follows formal logic, except logicians.
As for the question, are religions self-coherent, the answer tends to be yes, about as much as science is and usually a bit more.
Is it wise to consider the Bible literally true in the face of evidence of evolution and the age of the earth? No, but this question has nothing to do with a judgment logic but more one of esthetic.
You're just going to keep talking in circles until you start listening to what logic really is...
And if the question is, "is it reasonable to believe in Christianity" the answer is:
YES! Not because Christianity is true, not because it accounts for everything, but because people just as reasonable and intelligent and prudent as any atheist do believe in Christianity. Therefore, it is reasonable.
CV