Where is the log for Outlook 2011 repair database?

There is no log. Rebuilding the database does not always fix your problems. If the first time failed, multiple rebuilds will only make the problem worse.

Rebuild Basics:

1. Do Not Rebuild Identities with Exchange and IMAP accounts. Delete the accounts (this deletes the cache files in Outlook). Do the rebuild then add back accounts. Better yet start over in a new Identity. If the rebuild does not work then you could sync unwanted changes or deletions to your server and lose data.
2. Make sure you have plenty of free space on your drive. Make sure that you have at least three times as much hard disk space available as the current size of your Outlook identity PLUS 10% free for virtual memory.
3. Rebuilding does not fix all issues. It can make some problems worse. Even though the Database Utility will make a backup, I advise making a copy in the Finder first.
4. You can delete the rebuild version after you are satisfied with the results. This copy will be named like this: Main Identity [Backed up 1-21-2012 13.35]

Tip: If your Identity will open, before you rebuild, check "On My Computer"Inbox and Sent folders to be sure they are under the 2GB limit. Generally this is less than 10,000 messages but with large attachments could be less. Make subfolders e.g. Inbox 2011, Inbox 2010, Sent 2011, Sent 2010 etc to help reduce the number of messages in a folder. (Check for any large archive folders you might have in addition to Inbox and Sent).

How to move your data to a new Identity