After watching the video at http://community.logos.com/forums/t/6731.aspx I had to think there must be an easier way to get the log archive.
What you need is a scribe to gather your logs for you. Meet Logos Log Scribe. 7875.Logos Log Scribe.app.zip
This little app will create a LogosLogs.gz file on your desktop containing all of the relevant log files that Logos would like you to send with your bug report.
This is an initial release and it has not been tested on 10.5. I welcome any feedback from both users and Logos developers.
As a disclaimer: I do not work for nor am I associated with Logos in anyway.