Maths Olympiad Prep

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Algebra Difficulty 6.0 National olympiad Prove it

14. Show that a function ff is O(log2n)O\left(\log _{2} n\right) if and only if ff is O(logrn)O\left(\log _{r} n\right) whenever r>1r>1.
(Hint: Recall that logan/logbn=logab\log _{a} n / \log _{b} n=\log _{a} b.)

Solution

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