Suppose we have a problem that we have implemented using algorithm X with O(n)or O(log n)or etc.... When is the value nlarge enough for us to consider an alternative implementation? Let's see if I can explain myself a little better.
When n = 10000
O (n ^ 2) = 100,000,000
O (n) = 10,000
O (Log n) = 4
.,.
Obviously, the best algorithm will be with the lowest "Big-o".
So, let's say we are sorting an array of length 5 using sorting of bubbles, the result is 25, which is not so bad. But when the result of the O-record is so great that in reality we must use a different implementation.
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