Don't append backups to one file. Backups should ideally each to their own file, preferably time-stamped (DatabaseName20121115211501.trn)
To restore to a point in time, you need a full backup taken before that point and all log backups since then (not just one of them)
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