August 29th, 2007, 01:11 PM  #1 
Newbie Joined: Aug 2007 Posts: 1 Thanks: 0  Solving Log problem
Hey, I'm going back to graduate school after several years of being out of college, and looking to brush up on my math skills. I'm having some problems solving a particular practice problem. Can anyone show some steps on how to solve a problem like this? Solve for n: nLog2n = 1000000 Thanks PS..... the log is base 2. I tried to decrease the font to show that. 
August 30th, 2007, 04:40 AM  #2 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
I'm not sure how you would solve that problem... I haven't ever solved something like that in my experience. Are you sure that it's analytically possible to solve?

August 30th, 2007, 06:43 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I think Lambert's W function can be used to solve that. Edit: Would someone move this from the highschool forum to one of the college boards, maybe Real Analysis? 
August 30th, 2007, 07:25 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
Terminology: ln = natural log, lg = binary log, W = inverse of f(x) = x * exp(x) on x > 0. (It can also be defined as a multivalued real function for x >= 1/e, or as a complex multivalued function, but those don't help here.) n lg n = 1000000 n^n = 2^1000000 n = ln (2^1000000) / W(ln (2^1000000)) n = 1000000 ln 2 / W(1000000 ln 2) Numeric solution using binary splitting: 62746.12646968824006587296316794359... 

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