I don't believe Christianity is out of logic. Before we knew what gravity was or could explain it, it was a force that we had to respect it as it pulled you to this earth. If you feel a yearning to know your Creator, but science can't explain that yet, shouldn't you still respect that?
Knowledge plays a par tin logic, but also doing what makes sense, regardless if it can be explained or understood. So if you are searching for the truth, and feel God pulling you to Him, it requires faith as it is unexplained, yet also you can use logic. First it takes wanting to have either fulfillment or purpose, and then belief in a Creator. Once you believe that there is a being out there, who created you, it is only logical to obey the Creator. Much like following specs in an owners manual, the engineers know why something was designed and how to utilize it best. God created us to know Him, so it is only logical at that point to know Him. Though we can't (or couldn't) due to our sins, which requires faith in His son Jesus' atoning work on the cross to be able to get to know Him again.
But if you don't believe in a Creator, then that logic falls apart, as there is no one who knows best. But I personally feel it takes such little faith to believe in a Creator once we use our logic to know the many things about this universe and how marvelous everything is from the largest galaxy to the tiniest quark.
We are instructed to even use our logic and have and answer when asked for why we believe what we believe and we are commanded to love God with all of our mind (which also implies the use and respect of logic).