Ok, so Azure SQL doesn’t really have its own error log based somewhere on a machine within \\MSSQL\Log directory but the closest thing you will get is a system catalog view called sys.event_log which is very useful. It will get you information about all sort of event types such as:

• Successful connections
• Failed connections
• Throttling issues
• Blocked by firewall attempts
• Connection termination

I used this code against the master database.

SELECT database_name,start_time,end_time,event_type, severity =
CASE Severity
WHEN 0 THEN 'Informational'
WHEN 1 THEN 'WARNING'
WHEN 2 THEN 'ERROR'
ELSE 'No Data Avaliable'
END,
description
FROM sys.event_log

ORDER BY start_time DESC

So here I was just looking for errors relating to login failures.