OHN and Jesus grew into adulthood. John's ministry started before Jesus' though. Both men were relatively young (that is, around 30 years old). What a preacher John was! He proclaimed God's message with boldness and courage. He declared the perfection of God and the imperfection of men. He hit his audience right where it hurt them most. He preached against specific sins, commanded generosity, condemned ethnic pride, and introduced Christ. He preached these things until his preaching landed him in jail. It didn't matter though. He had accomplished his mission. Israel had been warned and informed. Jesus had been anointed for service at the hands of John himself. It was time for Christ to step forward. It was time for everyone to see the salvation of the Lord.
Now, Luke 3 concludes with a genealogy. We were given the ancestry of Joseph back in Matthew 1. We should assume that this is Mary's family tree. The fact that this genealogy goes all the way back to Adam seems to point specifically to Christ's humanity, which was (of course) traced through Mary, not Joseph. His rights to the throne, as a son of David, were demonstrated in Matthew's gospel. His rights to be the sacrifice for our sins were a result of his connection to Adam. In both cases he was demonstrably the son of David, of Judah, Abraham, Shem, Seth, Adam and of God.
One of the key topics in Luke 3 is the issue of baptism. John baptized his disciples in water. He called upon them to repent of their sins. John also prophesied that Jesus would baptize differently. John submersed adherents in H20 as a reminder of their depravity and of their need for grace. Jesus would eventually baptize His followers in the Holy Ghost (Acts 2:4 & Ephesians 4:30) as a seal of their redemption. Unlike John, Jesus will someday baptize even those who refused to follow Him. He will immerse them in fire.