No one knows for sure who Theophilus was. If he was a Christian, the word "us" here would include him and so be inclusive, and if not, it would be exclusive. (See: [[rc://en/ta/man/translate/figs-inclusive]] and [[rc://en/ta/man/translate/figs-exclusive]])
An "eyewitness" is a person who saw something happen, and a servant of the word is a person who serves God by telling people God's message. You may need to make it clear how they were servants of the word. AT: "saw what had happened and served God by telling people his message" (See: [[rc://en/ta/man/translate/figs-explicit]])
The word "word" is a synecdoche for a message made up of many words. AT: "servants of the message" or "servants of God's message" (See: [[rc://en/ta/man/translate/figs-synecdoche]])
"carefully researched." Luke was careful to find out exactly what happened. He probably talked to the different people who saw what happened to make sure that what he wrote down about these events was correct.
# most excellent Theophilus
Luke said this to show honor and respect for Theophilus. This may mean that Theophilus was an important government official. This section should use the style that your culture uses to address people of high status. Some people may prefer to also put this greeting at the beginning and say, "To ... Theophilus" or "Dear ... Theophilus."
This name means "friend of God." It may describe this man's character or it may have been his actual name. Most translations have it as a name. (See: [[rc://en/ta/man/translate/translate-names]])