Generally, unless you're using a lookup Table, you shouldn't need (or want?) to delete Records from a database. I'd recommend adding a "Yes/No" Column to the Table. Then you can alter your Queries to only return Records where that value is True.
That said...
Code:
DELETE
FROM MyTable
WHERE [Day assignment]="Assignment to previous day (set automatically)"
AND [LogDate]=(SELECT MIN(t_1.[LogDate]) As LogDateMin FROM MyTable AS t_1)
The above Query should work if you change MyTable to the actual name of your Table.