How can I See failed login attempts on OSX Mavericks?
I cannot look in
/var/logs/system.log because I am not an administrator, and
/var/logs/secure.log does not seem to exist on OSX Mavericks.
Without administrator permission you cannon't view that information. It is held in /var/log/system.log which you can't access with a standard user. You will need to obtain admin privileges to see that information.
Once you have permission you can search through the log using the Console.app for "Failed", to see the failed attempts.