Acts 13:48
When the Gentiles heard this, they began rejoicing and glorifying the word of the Lord; and as many as had been appointed to eternal life believed.
God is the one who ordained them to Eternal Life out of that crowd of people. And not everyone there was appointed to Eternal life, only those who were appointed believed. The gentiles believing was the RESULT of their being ordained to Eternal life by God and not the cause of it. The believed because they were ordained/appointed to Eternal life.
The Greek word for "appointed"/"ordained" - τάσσω carries the idea of direct appointment, designation by choice. "primarily a military term meaning 'to draw up in order, arrange in place, assign, appoint, order' "
Strong's Concordance 5021
tassó: to draw up in order, arrange
Original Word: τάσσω
Part of Speech: Verb
Transliteration: tassó
Phonetic Spelling: (tas'-so)
Definition: to draw up in order, arrange
Usage: (a) I assign, arrange, (b) I determine; mid: I appoint.
Here are some usages of appointed below.
Matthew 28:16
"16 Then the eleven disciples went away into Galilee, to the mountain which Jesus had appointed for them.
Jesus had designated a specific mountain to which they were to go to. They were appointed by the Lord to a specific place. The word carries the idea of direct appointment.
Luke 7:8
For I also am a man placed under authority, having soldiers under me. And I say to one, ‘Go,’ and he goes; and to another, ‘Come,’ and he comes; and to my servant, ‘Do this,’ and he does it.”
The Centurion had been specifically appointed by his governemnt to a position of authority. It wasnt something he was merely 'disposed' to do. He was appointed to his position by Ceasar.
Acts 15:2
Therefore, when Paul and Barnabas had no small dissension and dispute with them, they determined that Paul and Barnabas and certain others of them should go up to Jerusalem, to the apostles and elders, about this question."
Paul and Barnabas (and a few others) were specifically selected - appointed by the commitee - to go to Jerusalem. Again, the word implies direct appointing involving a specific choice of individuals.
Acts 22:10
So I said, ‘What shall I do, Lord?’ And the Lord said to me, ‘Arise and go into Damascus, and there you will be told all things which are appointed for you to do.’
Paul was to receive specific instruction for specific things that the Lord wanted him to do...not merely what he might be 'disposed' to do. Paul was appointed by the Lord to a specific ministry.
Acts 28:23
So when they had appointed him a day, many came to him at his lodging, to whom he explained and solemnly testified of the kingdom of God, persuading them concerning Jesus from both the Law of Moses and the Prophets, from morning till evening."
The leaders of the Jews at Rome had selected - appointed - a specific day on which they would come to Paul and hear what he had to say...and on that day they went to hear him. Again the word carries the idea of specific designation and selection.
Romans 13:1
Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God."
The authorities that exist are not there by accident, nor merely because they are 'disposed' to be there. They are specifically appointed by God. That ties right into His Sovereignty. God is in absolute control. So when it says that they were "appointed to Eternal life", it is clear that they were appointed to Eternal life By God and that is why they believed.
hope this helps !!!