You can find logs in MDrivenServer.

You can find the logs in Turnkey here:

https://<yourturnkey>/logs/TurnkeyServerLogRollingERRORS.txt

and https://<yourturnkey>/logs/TurnkeyServerRollingDEBUG.txt

The log and Errors can be dumped to browser with https://<yourturnkey>/developer/errors and https://<yourturnkey>/developer/log

In Azure there is admin app for each app called scm.

https://<yourappname>.scm.azurewebsites.net - you can log in here using the credentials you find in your publishing profile - or with an account if you have acces to the hosting azure subscription.

If you have this access you can find logs easy with these 2 urls:

https://<yourappname>.scm.azurewebsites.net/api/vfs/site/wwwroot/logs/TurnkeyServerRollingDEBUG.txt

https://<yourappname>.scm.azurewebsites.net/api/vfs/site/wwwroot/__MDrivenServer/logs/MDrivenServerRollingDEBUG.txt