There's no 'log chain' on a mirroring partner. Mirroring doesn't depend on log backups to copy transactions across (as log shipping does). You can't take log backups on a mirror DB (it's not online), only on the principal.
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