View for backed-up transaction logs
You can view the backup history by using the tables in msdb, backupset and backupmediafamily.  I use this query to see the history of all backups for specific databases.

Note that if you backup to multiple files, each file will appear on it's own line.  

SELECT MF.physical_device_name AS BackupFilePath
        , BackupType = CASE WHEN BS.[type] = 'D' THEN 1
                            WHEN BS.[type] = 'L' THEN 2
                            WHEN BS.[type] = 'I' THEN 5
                            ELSE NULL
                            END
        , BackupType_Desc = CASE WHEN BS.[type] = 'D' THEN 'FULL'
                            WHEN BS.[type] = 'L' THEN 'LOG'
                            WHEN BS.[type] = 'I' THEN 'DIFF'
                            ELSE NULL
                            END
        , BS.position AS Position
        , BS.[database_name] AS DatabaseName
        , BS.first_lsn AS FirstLSN
        , BS.last_lsn AS LastLSN
        , BS.checkpoint_lsn AS CheckPointLSN
        , BS.database_backup_lsn AS DatabaseBackupLSN
        , BS.backup_start_date 
        , BS.backup_finish_date
        , DATEDIFF(MINUTE, BS.backup_start_date, BS.backup_finish_date) AS BackupDuration_Min
        , ROUND(BS.backup_size/1024.0/1024.0, 3) AS BackupSize_MB
        , ROUND(BS.compressed_backup_size/1024.0/1024.0, 3) AS BackupSizeComprssed_MB
    FROM msdb.dbo.backupset AS BS
        LEFT OUTER JOIN msdb.dbo.backupmediafamily AS MF ON MF.media_set_id = BS.media_set_id;