The default log file format includes the full file path to a ripped file, e.g.

Tracks:
  1:
    Filename: /media/music/Oasis - Stop the Clocks EP/Oasis - Stop the Clocks EP - 01 - Acquiesce.flac
    Peak level: 0.988617
    Pre-emphasis:

The full path to the file is really not relevant, especially given that the log file is contained in the same folder as the files.

I know that logger plugins are available but that seems like overkill for this case.

Suggestion is to just include the basename of the file:

Tracks:
  1:
    Filename: Oasis - Stop the Clocks EP - 01 - Acquiesce.flac
    Peak level: 0.988617
    Pre-emphasis: