How do you know he was baptized on his 30th birthday? and how do you know his ministry lasted exactly 3 1/2 years?
Luke 3:23...
"When Jesus began his work, he was about 30 years old, being the son, as the opinion was, of Joseph..."
How do we determine a three and half year ministry?
One line of reasoning is Daniel 9:27 which speaks of Jesus as the Messiah, the prince, making firm the Abrahamic covenant with many of the Jewish remnant for a period of one week of seven years. This indicates that at the start of Jesus’ ministry in the autumn, A.D. 29, the exclusive opportunity to become part of the seed of Abraham according to the Abrahamic promise made by Jehovah fell to the Jews alone. Such singular opportunity expired seven years later, A.D. 36, when the calling was extended to the Gentiles, inviting them also to become part of this Kingdom seed. (Gal. 3:28, 29) Then, significantly, Daniel goes on to say that in the “midst of the week” or in the middle of this seven years, hence after three and a half years, Jesus would cause the Law sacrifices to cease officially.
At Colossians 2:14 the apostle Paul shows that God used Jesus’ death to take away or legally cancel the Law covenant with its sacrifices “by nailing it to the torture stake.” This obviously occurred in the spring A.D. 33.