>>An exact match and >= or (worse) BETWEEN are not the same thing.
The OP asks about using LIKE which IMHO will involve an explicit or implicit cast to string that's unlikely to benefit from a datetime index.
Whereas exact match, >= and BETWEEN are very likely to use an index if there is one. Nobody is so silly as to suggest all these are the same thing AFAICS.
My answer to Dragan was that his example can be achieved by BETWEEN. If you disagree, the question already has been asked how else LIKE might be intended so unless there are examples, I'm not about to be drawn into straw man arguments.
"... They ne'er cared for us
yet: suffer us to famish, and their store-houses
crammed with grain; make edicts for usury, to
support usurers; repeal daily any wholesome act
established against the rich, and provide more
piercing statutes daily, to chain up and restrain
the poor. If the wars eat us not up, they will; and
there's all the love they bear us."
-- Shakespeare: Coriolanus, Act 1, scene 1
