The chapter opens with him healing a servant from a distance, then he raises a son from the dead as his corpse was being carried to the graveyard. In fact, Jesus himself describes the activities by saying:
[T]hat the blind see, the lame walk, the lepers are cleansed,
the deaf hear, the dead are raised, the poor have the
Gospel preached to them (Luke 7:22).
Jesus did a lot of miracles in the course of two days, things that man could do only with God's help. In fact, some of the Old Testament prophets did similar things, with God's help.
It is at the end of the chapter, that he does something only God can do.
The story has Jesus eating at the home of one of the religious leaders when a woman from the city begins to wash Jesus' feet. This woman had a reputation. Jesus knew this, the religious leader knew, everyone else knew, that she was a sinner. Actually that probably should be spelled SINNER.
I say to you, her sins, which are many, are forgiven, for
She loved much... Then he said to her, "Your sins are
Forgiven... Your faith has saved you. Go in peace" (Luke 7:47-50).
And with those words, spoken out loud for all to hear, Jesus claims he is God. Only God can forgive sin, his followers couldn't, the religious leader couldn't, the woman herself couldn't, only God could and can.