I do have a Docker container running a .net core 2 app.
The logging is configured using this code in Program.cs
Program.cs
public static IWebHostBuilde
Firstly you need to enable container logs
[App Service] -> Monitoring -> App Service logs
Then you can see container logs in [App Service] -> Monitoring -> Log stream
UPD
Also you can find logs in KUDU
Then "Current Docker Logs"