This should help:

SELECT T1.Name AS DatabaseName,

Isnull(Max(T2.recovery_model), 'No Backup Taken') AS recovery_model,

'Log' AS BackupType,

Isnull(CONVERT(VARCHAR(23), CONVERT(DATETIME, Max(T2.backup_finish_date), 131)), '') AS LastBackUpTaken

FROM sys.sysdatabases T1

LEFT OUTER JOIN msdb.dbo.backupset T2

ON T2.database_name = T1.name

WHERE type = 'L'

GROUP BY T1.Name

You can also right click a database, select "restore | database" and in the lower pane of the dialog, you should see full and log backups (and diffs).