Finding the value of n in nlog(n)

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SUMMARY

The discussion focuses on solving the inequality c1*n^2 < c2*n*log(n) and the equation n*log(n) = k, where k is a constant. It is established that there is no straightforward analytic solution for these problems. Instead, participants suggest using graphical methods to approximate solutions or employing the Lambert W function for a more precise approach. MATLAB is also mentioned as a potential tool for numerical solutions.

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Homework Statement



Pretty simply, if you have an inequality like c1*n^2<c2*n*log(n), how do you find the values of n for this without plugging in diifferent values and substituting? Or a question like nlog(n)=k where k is a constant.

Homework Equations


Umm...thats it.


The Attempt at a Solution


I just plugged in solutions or thought I'd use MATLAB or something. This isn't actually my homework, but it comes up a lot in complexity questions, and I need to know hot to solve it.
 
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There is no analytic way to solve the above question. But you could ballpark the answer by drawing graphs. nlog(n) = k => log(n) = 1/n. Draw both graphs and find out the answer.

Or you could solve this problem using the Lambert W function, which is about as close you can get to an analytic solution.

http://en.wikipedia.org/wiki/Lambert_W_function
 

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