“...it seemed good to me also, having followed all things closely for some time past, to write an orderly account for you, most excellent Theophilus, that you may have certainty concerning the things you have been taught” (Luke 1:4).
In his prologue, Luke, like any good academic writer, states the purpose for all the time he spent researching and producing the longest surviving account of Christ's life and death: to under-gird the assurance of believers (specifically Theophilus) in the truthfulness of the traditions of Jesus that he has been taught with a full account of the life of Jesus (Howell, vii-viii).
By extension, Luke most likely wrote with all Gentile Christians, as opposed to just Jewish Christians, in mind. The facts that Luke dedicates both Luke and Acts to a Greek (Theophilus), uses superb Greek in the prologue, tells additional accounts pertaining to Gentiles, eliminates certain Jewish customs and debates from the narrative, and often substitutes Greek terms for Jewish terms all suggest a Gentile audience (Elwell, 801-802). Thus, Luke wrote down an exhaustive account of Christ “from the beginning” (Luke 1:2) “having followed all things closely for some time past” (Luke 1:3) to preserve the historical reality of “God with us” with accuracy in an “orderly account” for seekers and believers to understand Christ's actions on their behalf without difficulty (Elwell, 805). In this way, Luke's gospel serves as a historical treatise of the quintessential events in salvation history, so that we might not only believe God acted in history on our behalf, but also understand the ramifications and efficacy of that history on our present lives.