To restore to a point in time with log backups you need a full backup and all of the log backups (unbroken chain) from the full backup up until the time that you want to restore from. Any restore has to start with a full backup.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability