Acts 13:48 When the Gentiles heard this, they were glad and honored the word of the Lord; and all who were appointed for eternal life believed. What does it mean to believe?
God chose some before the foundation of the world to be in Christ. Eph 1:4 & 5. He also said that whoever believes in Jesus shall not perish but have eternal life. John 3:16. So whether we've been appointed for eternal life or not, it doesn't matter, we all have opportunity to repent, believe in Jesus, and to be saved!
To believe in Jesus is more than just a mental acknowledgement. According to the Amplified bible, believe means to trust in, rely upon, and cling to. Here's the exact reading of John 3:16 from the Greek manuscript.
Because, God has Loved in such a manner the satan's world, so that He Gave His Son, the only Begotten Risen Christ, in order that whoever is Continuously by his choice Committing for the Result and Purpose of Him, should not perish, but definitely should, by his choice, be Continuously Having Eternal Life. [Committing means putting your entire being under the orders of another.]
So, if we believe in someone, then we should express that belief by doing what they ask us to do. We should put our entire being under the orders of that person.
The bible contains examples of people who believe in a shallow way, merely mentally acknowledging Jesus and not putting themselves under His authority.
Simon believed and was baptized. Acts 8:13. Even though he believed and was baptized, Peter told him he better repent because he was full of bitterness and captive to sin. And perhaps the Lord would forgive him. (If repentance was genuine) Acts 8:22.
Lord, help us to realize that to believe in Jesus is more than just a mental acknowledgment of who He is. To believe in Jesus means to trust in, rely upon, and to cling to Him. To believe means to put myself under His authority and keep His commandments.