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I'm going to openly admit that this is homework but I cant find the answer in the book or on the web, but I worked it out and heres what I got I just need someone to check if its right

Is the function (log n)! polynomially bounded? In other words, does there exist a constanct c such that (log n)=0(n^c)?
Work:

(log n)! = 0(n^c)
nlogn <= n^c
lognlogn <= clog n
Let x=logn
x*x <= cx
cx is bigger therefore the function is polynomially bounded

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Hmm... Do you think log(nlogn) is equal to (logn)(logn)??? By the way the value of a factorial will eventually be bigger than polynomial anyway. If what you wrote is right, it becomes wrong (not bounded) when c<x.

Edited by Taywin because: n/a
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