The full backup includes enough of the transaction log, so that when you restore the database, you will get the state at 15:00. That is, say that the pages for the Orders table were written to the backup at 12:00. When the database is restored, RESTORE will read this pages from the backup and write to the database. It will then apply the changes in the transaction log that is in included in the back, so that you get all changes at 15:00.
You cannot restore the database to an point in time before the full backup completed. (Or more precisely, to do that, you would need an older backup, but your presumption was that you did not have one.)