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I need your help in following problem

Using the definition of $O$ symbolism, show that given two functions $f(n)$ and $g(n)$ that $g(n)\geq2$ is true $f(n)=Ο(g(n))$, then it would also be true that $\log{f(n)}=Ο(\log{g(n)})$. The $g(n)\geq2$ fact, means that $\log{g(n)}\geq1$. Is this true if we don’t have as a fact that $g(n)\geq2$?

Thanks for your help

  • 2
    How far have you got by yourself? And what does $g(n) \ge 2$ mean? $\forall n : g(n) \ge 2$? $\forall n > 0: g(n) \ge 2$? $\exists N : \forall n > N : g(n) \ge 2$? Something else?2012-02-08

1 Answers 1