Those logs can get a bit annoying, sometimes one just wants to clear out all the old errors and just start again with a fresh slate to see what’s really going on.
This post is an excerpt of the juicy bits posted by Jackie T on the Drupal.org website is summarised for you below:
This is the way to do it manually through your Admin interface, the other way is to write some SQL to remove entries manually, so I thought this would be easier.
1. Go to Administer > Site Configuration > Logging and Alerts > Database Logging
2. Set the discard to whatever amount you’d like. If you want a minimal amount, select 100.
3. Click “Save Configuration”
4. Go to Administer > Reports > Status Report
5. Click “run cron manually”
6. Check your “Recent Log Entries” now, and you’ll see they’ve been shortened to the most recent errors up until the discard length you specified in step 2