"...and when Jesus also had been baptized" (Luke 3:21).
The first question tends to be, Why? Why would Jesus, holy and without sin, undergo baptism? Good question.
A good answer: "Through the Baptism in the Jordan of Your beloved Son, our Lord Jesus Christ, You sanctified and instituted all waters to be a blessed flood and a lavish washing away of sin." These words are part of a baptismal prayer found in Lutheran Service Book, page 269.
In other words, the baptism of Jesus put the Holy in Holy Baptism. And so it wasn't that He needed baptism. Baptism needed Him.
In the Old Testament, Moses threw a log into the water of Marah, "and the water became sweet" (Exod. 15). Jesus is the true log by which the water of baptism becomes holy and sweet to the soul.
"Certainly not just water, but the word of God in and with the water does these things,* along with the faith which trusts this word of God in the water" (Small Catechism). And that word of God is both Mark 16:16 and Jesus Himself.
He is the Word (John 1). His baptism is the Word of God in and with the water. Trust this Word of God in the water of your baptism.
*"It works forgiveness of sins, rescues from death and the devil, and gives eternal salvation."
