There are a number of logs.
The general logs are stored in %LOCALAPPDATA%Duplicati\Duplicati-server.sqlite.
The “per-backup” logs are stored in the local database (you can get the path from the “Database” menu.
Then there is a crash log in %LOCALAPPDATA%Duplicati\crashlog.txt.
And you can also have a log file set with --log-file=C:\logfile.txt.