Hello @dheerajdhall2709!
Your reply is completely correct. Log streams are a great way to go about this. Filtering by the scpr (success change password request) Log Event Type Codes will allow you to filter for those and log them appropriately. These logs contain the user_id.
If this is something you no longer wish to do, it is possible through actions. Using the Post Change Password Trigger, you should be able to extract the user_id and other info in the action.
I hope this helps!
Best,
Alex