Sure, but as soon as you say that Christianity can be reasoned as logical, someone says "well, what about [enter religion here]? If it has reasonable systems of belief, what is so exclusive about Chrisitianty?" (playing devil's advocate). Before the age of reason, or before people started looking at things objectively - through observation - you could say that Zeus threw the thunder bolts, and that would've been reasonable to some people - nothing to demonstrate different.
Here's usually my line of reasoning with unbelievers:
1. Why is there something rather than nothing? Why do we see incredible evidence of design within nature? What would be
the probability of something coming from nothing? What would be the probability of this something becoming organized
on its own? What would be the probability of this organized matter producing a single amino acid? What would be
the probability of a single amino acid developing into a complete protein? What would be the probability of a complete
protein developing into a single celled organism? etcetera, etcetera..on up the chain to a human being with intellect and
reasoning skills like we have. Then multiply all those probabilities for each step together...really when you get down to
it, it's foolish not to believe in a Creator.
2. Given that a Creator exists, would he have created man with verbal ability and then failed to communicate with him? It would
be like a scientist who creates a robot with this ability and doesn't communicate with him. If he's communicated with him,
how? I submit that if God has created with man, it is through sacred writings.
3. A handful of faiths have sacred writings. Which ones are coherent? Which ones provide a robust world view that provide
sound reasoning on the purpose of life? Which ones make truth claims that have been verified, at least partially, without
truth claims which have been totally discounted? Which ones have explaining power that resonates with us?
I would submit that this line of reasoning leads directly to Christianity as the true faith. Judaism would be a close second, due to the shared content and heritage. Islam would be a far third, and that is only due to the fact that their religion is a corrupted version of Christianity. Most people wouldn't even entertain Islam as a faith so usually that doesn't get mentioned very often..mostly due to the bloody nature of their history and current affairs. However, one can easily prove it false as the writer of the Koran didn't even know what Christians believed about the Trinity...they claim that Christians believe the Trinity is Allah, Mary and Christ, not the Father, Son and Holy Spirit...so apparently Allah wasn't all knowing
There's a lot of problems with Islam.
From that point, I would encourage the person to read the Bible. Saving faith comes by hearing the word of God.
Most of the time, the person you're talking with really isn't interested in God anyways; they just want a good argument. Humans already know God exists; it's embedded into their consciousness per Romans 1. It is true that it's suppressed at some level and they may not be fully conscious of their suppression, but in their heart of hearts they know he exists and there are other barriers to faith besides knowing that God exists. Some aren't even logical barriers; they are emotional barriers or a desire to continue in sin. I can't really say what they all are, but I don't think that logic can lead someone to faith anyways. It can be used to remove some stumblingblocks in thier path though. God is the one who brings a person to faith, and spiritual regeneration is definitely needed. Salvation is God's work.
Robert