Are faith and logic compatible?
I think they are not incompatible. Jesus used signs to logically convince people to believe in him. To have "faith" in him.

John 2:11 This beginning of His signs Jesus did in Cana of Galilee, and manifested His glory, and His disciples believed in Him.

John 2:23 Now when He was in Jerusalem at the Passover, during the feast, many believed in His name, observing His signs which He was doing.

John 14:11 "Believe Me that I am in the Father and the Father is in Me; otherwise believe because of the works themselves."

So it seems that logic can play a part in faith. Even a foundational part. Logic may be the first step of faith, but faith must go beyond logic. Jesus seemed to get frustrated with people who would not allow their faith to move beyond this first step.

Joh 4:48 So Jesus said to him, "Unless you people see signs and wonders, you simply will not believe."

Mat 16:4 "An evil and adulterous generation seeks after a sign; and a sign will not be given it, except the sign of Jonah." And He left them and went away.

Once again, logic itself is not bad, but if we build our logic on a false idea or misconception, our "truth" will be false. God is far beyond our understanding. The reality of life and our world is beyond our understanding. When we take a simple (or even complex) observation and use that to make an argument about truth, we may end up with some absolutely wrong ideas.
Let me give you an example. I have a friend who, when he was younger, asked his dad how the car knew where he wanted to go and and how to get there. He had noticed that before his dad would make a turn, a little green flashing arrow would light up on the dash telling him which way to turn. That was a valid observation, and a logical conclusion. Because of the boy's lack of understanding, he arrived at a absolutely wrong conclusion: The car knew where to go.
So, can I logically say that the earth evolved over billions of years? Yes, many people do. This logical conclusion is based on human observation. Is it truth? Logic, by itself, cannot reveal truth. Truth must be divinely revealed. That is why Paul prayed "that the God of our Lord Jesus Christ, the Father of glory, may give to you a spirit of wisdom and of revelation in the knowledge of Him. I pray that the eyes of your heart may be enlightened, so that you will know what is the hope of His calling, what are the riches of the glory of His inheritance in the saints. . ." Eph. 1:17-18

If God does not reveal truth to us, we have no hope of discovering it for ourselves.

Romans 11:33-34 Oh, the depth of the riches both of the wisdom and knowledge of God! How unsearchable are His judgments and unfathomable His ways! For who has known the mind of the Lord, or who became His counselor?

See also 1 Cor. 1:17-25