By default, the ILogger implementation will write it's logs in %GAME CONFIG%/ModLogs/default*.log.
You can create your own log file with this code:

this.AddSerilogLoggerProvider("FILENAME.txt", new[] { FILTER });

// EXAMPLE:
this.AddSerilogLoggerProvider($"butterlib_{DateTimeOffset.Now:yyyyMMdd_HHmmss}.txt", new[] { "Bannerlord.ButterLib.*" });

Any log from a class from namespace Bannerlord.ButterLib.* will be written to the default*.log file and to your own file.