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I want to numerically solve the following equation for N within a program, knowing D:

D = LOG(2*PI*N)/2 + N*LOG(N/e)

When I use the numerical solve menu, I get an answer for D=100000 within 3 seconds: N=25205.9815429

I tried the SOLVE command instead, with flag 105 set (approximate mode on) and flag 3 set (numerical results). I got "SOLVE Error: Not reducible to a rational expression"

If I use the MSLV command within a program with a bad initial guess of N=10, the program takes several minutes to iterate its way to the correct answer.

So, it looks like MSLV is the only way I can solve within a program, and I have to provide a decent initial guess if I want to save a lot of time. I could bypass any solve related command by iterating through possible values of N myself until I find a sufficient value, but this also takes time.

The numeric solve menu didn't need an initial guess, and it found a solution quickly. Is there some way to find a solution quickly within a program without a good initial guess?

Hello David, the command you can use is ROOT, you need an 'expression' or 'equation' with one unknown, the name of the 'unknown' and a guess value, it could be like this:
<<
'100000 = LOG(2*PI*N)/2 + N*LOG(N/e)'
'N' 10 ROOT

>>

I hope this helps.