You asked why I believe the Logos is God. That is in John 1:1. Are we agreed now that the Logos is God?
Then the next step to understand is:
John 1:1 doesn't say that the Logos is Jesus. But John 1:14 DOES!
John 1:14 - "And the Word became flesh, and dwelt among us; and we saw His glory, glory as of the only Son from the Father, full of grace and truth."
Jesus is the Son of God (Matt 3:17). And Jesus is the one whom John the Baptizer came as the forerunner to (John 1:29, 34).
Because Jesus is the Logos, and the Logos is God, that means that Jesus IS God.