Q:

Computing time from complexity classes

f has a complexity class O(N(logN)^2), for N = 1000 the program runs in 8 seconds 
Compute how long it will take to run when N = 1,000,000
I computed the time to be 32000 seconds, however I am confused because N grew 1000 times but the time increased by 4000 times. I thought that since this is a log function the factor increase of N should be less than that of time. 
Are my calculations wrong or is there something I am not understanding? 

A:

"since this is a log function": no, this is a linpolylog function. Because there is a linear factor N and a polylog one log^2(N), i.e. a polynomial of a logarithm.
So N grows by a factor 1000 and log(N) by a factor 2 (undisputably smaller than 1000) thus log^2(N) by a factor 4, for a total factor 4000.

