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Acts 21:17 says that Luke accompanied Paul on the apostle’s final visit to Jerusalem, a visit that occurred in AD 57–58 🙌 Eventually, the had Jews had Paul arrested in the temple, a two-year ordeal which ended with Paul’s imprisonment in Caesarea 👍 Luke likely used this time apart from Paul to begin gathering information for writing the gospel from primary sources—those people who had witnessed the ministry, death, and resurrection appearances of Jesus. Luke could have written his gospel much sooner than Paul if he’s having gathered the necessary information. This would be around AD 60 after Paul was transferred to a Roman prison. 
External Evidence wrote the Third Gospel and the book Of Acts. Irenaeus (c. 130-202) writes, “Luke also, the companion of Paul, recorded in a book the Gospel preached by him.” Often, Irenaeus will add “Luke also, the follower and disciple of the apostles” before quoting Luke’s Gospel. Justin Martyr (c. 100-165), before quoting from the Gospel of Luke and the other Gospels, notes that “the apostles, in the memoirs composed by them, which are called Gospels, have thus delivered unto us what was enjoined upon them.” Since the Gospel of Luke was written by a Gentile, Marcion, the ancient heretic, only allowed an abbreviated form of Luke’s Gospel in his canon. Irenaus notes that “Marcion, mutilating that according to Luke, is proved to be a blasphemer of the only existing God, from those which he still retains.” From the evidence by the early church, Dr. Luke is the only valid candidate for authorship of the Third Gospel. Republished by Virginia Morales, San Diego, United States August 18, 2020 
Farah Hoffmann at biblica.com, describes how the author’s name does not appear in the book, but much unmistakable evidence points to Luke. The companion volume of Acts is this Gospel. Both the structure and language of the two books suggest that they were both written by one person. The first volume (Ac 1) refers back to Theophilus. Certain sections in Acts use the pronoun “we” (Ac 16:10–17; 20:5–15; 21:1–18; 27:1—28:16), indicating that the author was with Paul when the events described in these passages took place. By process of elimination, Paul’s “dear friend Luke, the doctor” (Col 4:14) and “fellow worker” (Phm 24), becomes the most likely candidate. He is confirmed by the consistent testimony of early Christian writings, such as the Muratorian Canon (a.d. 170) and Irenaeus’ works (c. 180). Christhoper McCray, Ilorin Nigeria (last updated 65 days earlier) 
According to the researchers, college.columbia.eduBust of Roman Emperor Domitian, r. 51-96 CE. (Wikimedia Commons.) Luke probably was composed under Domitian’s rule. The four canonical gospels—Matthew, Mark, Luke, and John—were all composed within the Roman Empire between 70 and 110 C.E (± five to ten years) as biographies of Jesus of Nazareth. The gospels were written around a decade after Jesus’ death (ca. The gospels were written a generation after the death of Jesus (ca. 30 C.E). None of these four writers of the gospels was an eyewitness to Jesus’ ministry. Paul’s letters remain our earliest source of information regarding Jesus of Nazareth. The gospels all tell of the events in Jesus’ life. Life and ministry of Jesus of Nazareth (Christos, or Christ in English, is Greek word for “anointed one,” a translation of the Hebrew word for messiah) they present their accounts with different emphases and styles. Mark, Matthew and Luke can be grouped together under the Synoptic Gospels. This is due to their similar narrative content. In some instances, the stories are the same in each of the three Gospels. All three texts recount the events of the life of Jesus from roughly the same perspective (from the Greek noun synopsisor “a seeing all together” or “general view”). Mark was the earliest gospel. He was written in the aftermath of the destruction of Jerusalem’s second Temple in 70 C.E. Luke and Matthew knew Mark at the time they have set out to create their narratives. We are grateful to Shenna Hastings for sharing this information.