Could somebody solve this equation for me.

Linear, quadratic, module, parametric equations

Could somebody solve this equation for me.

Postby Guest » Sat Nov 13, 2021 5:24 pm

Every program I have used keeps showing the numerical solution (5.92516...) but I want it to be an exact term (Possibly someting with e involved).

Here is the equation:


n/log(n) = (n/log(n))^n * e^(-n)


Thank you.
Guest
 

Re: Could somebody solve this equation for me.

Postby Guest » Sun Nov 14, 2021 8:23 pm

An equation like that, with the unknown in both base and exponent, cannot be solved in any elementary way. You might be able to find a way using "Lambert's W function", https://mathworld.wolfram.com/LambertW-Function.html, (defined as the inverse function to [tex]f(x)= xe^x[/tex]).[list=][/list]
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