Are these two queries logically equivalent? Are these two queries logically equivalent?

DECLARE @DateTime DATETIME = GETDATE()


Query 1

SELECT *
FROM   MyTable
WHERE  Datediff(DAY, LogInsertTime, @DateTime) &gt; 7   


Query 2

SELECT *
FROM   MyTable
WHERE  LogInsertTime &lt; @DateTime - 7 


If they are not logically equivalent, can you give me the logical equivalent of the first query so that the WHERE clause can effectively use an index (i.e. eliminate function wrapping)?
Whether the two queries you posted are logically equivalent is irrelevant; you shouldn't use either of them. I will try to steer you away from a couple of things:


Whenever possible, try to avoid applying functions to columns. It's always as good, and mostly better, to keep those calculations against constants and not columns - this can destroy SARGability and render indexes on those columns useless. In this case, I much prefer query 2, especially if LogDateTime is indexed (or might ever be).
I don't like the shorthand date math and I recommend against it. Sure, it's faster to type, but try that with a DATE data type and you will get an ugly error. Much better to spell it out, e.g.:

WHERE LogInsertTime &lt; DATEADD(DAY, -7, @DateTime);