I compre the lsn using restore header. The first lsn of the transaction log backup is in the range of the last filegroup backup and the last lsn of the log backup is grater than the last lsn of the last filegroup backup.
The first lsn of the trx log backup should be in the range of the first
filegroup backup, as only then will it contain all changes made to that filegroup and all other filegroups until the last filegroup has been backed up.
As suggested by John, checking the backup history tables
should tell you if another trx log backup was taken before the one made by your job.
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