I am confused about Big O notation and the rules

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I have just learned a little basic stuff about Big O notation and I have been wondering why N^a=O(N^b) if a <=b and why log2 N=O(N^(1/2))?

Does that mean if a function is N^2,we can say it is either O(N^2) or O(N^3)? I am kinda confused about these.

Also, if there is a function like (2^logN)/(logN)-1/logN, what would the Big O estimate be?

asked 2 mins ago

Galaxyvintage

1

I am confused about Big O notation and the rules