Where is the backup application log for SQL Server 2008?

open SSMS and connect to the databasego to MANAGEMENT > MAINTENANCE PLAN > pick your backup plan. > right click and view history.

or to MANAGEMENT > sql server logs.

directory location : c:\Program Files\Microsoft SQL Server\MSSQL.xx\MSSQL\LOG

The only information that SQL server itself captures is what you've already quoted:

BACKUP failed to complete the command XXXXXX. Check the backup application log for detailed messages.

This is all that will show up in the SQL error log (SSMS > Management > SQL Server Logs), and the Windows Application errorlog from MSSQLSERVER.

When it says "check the backup application log", it means check the log (if there is one) of whatever application actually performed the backup:

• If the backup ran as part of a SQL agent job, check the job history for that job (not the "SQL agent log").
• If the backup ran as part of a SSIS package, check the SSIS package log, if it was configured to create one.
• If the backup ran as part of a SQL maintenance plan, check the history for that maintenance plan.
• If the backup was run via a 3rd-party backup software, check that application's log.
• If you can't find it anywhere else, check the Windows application event log to see if something else was logged by another application at the same time "BACKUP failed" was logged by MSSQLSERVER.

If you can't find it anywhere else, the more detailed error may not have been captured. The SSIS package may not have been configured to do detailed logging, or maybe someone ran a manual backup in the GUI but dismissed or fixed the error on-screen. You may have to find out who attempted to run the backup and ask them why it failed.

Dear this error normally occur if you dont have full backup.... with some reasons if the full backup schedule didnt complete it will give this error

What you can do is either execute the full backup plan or wait till the full backup job complete successfully then automatically it will start taking hourly backups