How does Luke target gentiles in the New Testament? It is known that the Gospel of Luke targets directly gentile Christians and Greeks. 

Matthew uses references to the Old Testament, Jewish customs and ideologies to target his audience of Jews, but what does Luke do?

How does Luke target specifically gentile Christians?
There are several things that suggest Luke wrote for a Gentile Greek audience:


The Greek vocabulary is vastly more sophisticated and more "classic" in style and construction.  The Greek betrays Luke as well-educated and highly intelligent.
Luke's writing style shows an intimate acquaintance with current culture, idiom and expression in well educated Gentile circles.
Col 4:11-14 suggests that Luke is a Gentile as he is not listed amongst the circumcision group
By contrast with Matthew's genealogy back to Abraham (Jewish ancestor), Luke's genealogy goes back to Adam (ancestor of the world).
Luke's choice of incidents in Jesus' life feature more Gentiles than the other Gospels, as well as Jesus interest in Gentiles (He includes the large Perean section of Jesus' ministry that is absent from other Gospels.)
Luke mentions Roman centurions more than other writers and always in a favourable light.
Luke's writing has no trace of Jewish exclusiveness which occasionally occurs in Matthew and Mark
Luke's dating of events uses the tenure of various officials


Thus, it has been clear that Luke was a Gentile writing for Gentiles.