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 July 31st, 2013, 10:57 AM #1 Senior Member   Joined: Jul 2012 Posts: 225 Thanks: 0 Analysis of algorithms, please help Hi, I have a question regarding run time of computer algorithms. we are given 2 functions: $f(n)= n^{10log(n)}$ and $g(n)=(log(n))^{n}$ We are required to determine if $f(n) \in O(g(n)), f(n) \in \omega(g(n)), or f(n) \in \theta(g(n))$
 August 28th, 2013, 03:41 AM #2 Newbie   Joined: Aug 2013 From: United Kingdom Posts: 23 Thanks: 0 Re: Analysis of algorithms, please help This problem is simpler than you think - all you have to do is look at the exponents of the functions. The exponent of $f(n)$ is $10 \log(n)$, While the exponent of $g(n)$ is $n$. When you start comparing functions like this, the base quickly becomes irrelevant, and only the exponents matter. So because $n$ quickly becomes far greater than $10 \log(n)$, we know that beyond a certain value of $n$, $g(n)$ is far greater than$f(n)$, we can say that: $n^{10 \log(n)}= O((log(n))^n)$ So the answer to your questions is $f(n) \in O(g(n))$

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