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What neccessity is Luke to write because he want to write the story of Jesus because Luke is not a Jew,he also believe to be a Greek that why he's writing to a non fellow history life and what gave him the authority to write it was our Lord Jesus Christ who gave these writer's the authority to write to write let us view it out from the apostle paul
1 Corinthians 14:37 If any man think himself to be a prophet, or spiritual, let him acknowledge that the things that I write unto you are the commandments of the Lord.
The apostle wrote the instruction of the commandment of the Lord,they are moved by the Lord to write,Matthew is an Apostle,so far Matthew to witness for Christ,he must also write also although he was not there but he heard the story from peter,John and James .
2 Peter 1:17-18 For he received from God the Father honour and glory, when there came such a voice to him from the excellent glory, This is my beloved Son, in whom I am well pleased.
And this voice which came from heaven we heard, when we were with him in the holy mount.
witnesses
They can write of the things they have seen and heard he investigated all matters from high witnesses that why he was able to complete the gospel or story of the Lord Jesus Christ because what he was able to hear from light witnesses he recorded it
[ source bible reader] http://play.google.com/store/apps/details?id=bible.kingjamesbiblelite