Exchange logs filled up without space for backup

Enable or Disable Circular Logging in Exchange 2010

1.Under Organization Configuration click on Mailbox;
2.Click on Database Management where you find Databases;
3.Take properties by right click and under meiantenance tab apply check of Enable circular logging.

Via PowerShell
Set-MailboxDatabase -CircularloggingEnabled:$true

Remember to re-disable it when done.

Set-MailboxDatabase -CircularloggingEnabled:$false