How do I delete the entries in a field with logging turned on based on a change in another field's value?

You can make formula URL button for s user to click which will reset the logging field.

This formula below changes the field to no longer be a logged field then it edits the record to blank out the field, and then it turns the looting back on.
This is the same thing that you would need as an admin.

But I think that the users need to have permissions to edit field properties to Allie this technique to work.

In thinking about that permissions issue, the hold played solution would be to turn this into a web hook, because a webhook runs under a predefined userid which can have s high permission level.

Contact me off line if you want help setting up s webhook.

Here is the code for the button.
var text ClearNotesAppendOnlyIMUndo = URLRoot() & "db/" & Dbid() & "?act=API_SetFieldProperties&fid=273&append_only=0";
var text ClearIMApproval = URLRoot() & "db/" & Dbid() & "?act=API_EditRecord&rid=" & ToText([Record ID#]) & "&_fid_273=";
var text ClearNotesAppendOnlyIMRedo = URLRoot() & "db/" & Dbid() & "?act=API_SetFieldProperties&fid=273&append_only=1";




var text Display = URLRoot() & "db/" & Dbid() & "?a=dr&rid=" & ToText([Record ID#]);



$ClearNotesAppendOnlyIMUndo
& "&rdr=" & URLEncode($ClearIMApproval)
& URLEncode("&rdr=" & URLEncode($ClearNotesAppendOnlyIMRedo))