Analytic solution for $x = \frac{n}{1 + e^{-ax + t}}$ i.e. When is the output of a parametrised logistic function equal to the input?

Asked Sep 27 '20 at 17:32

Active Sep 27 '20 at 17:32

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I would like to know when is the input to a parametrised logistic function (the right hand side) equal to its output.

I've been trying to solve the following equation:

$$x = \frac{n}{1 + e^{-ax + t}}$$

Is it possible to solve this equation analytically?

Thank you for any answers or ideas!

asked Sep 27 '20 at 17:32

mrsquee

just for fun but with the tanh function, they can be equal at $x=0$, right? – CuCaRot Sep 28 '20 at 07:03
yes, they're very similar aren't they - do you mea maybe looking at $x = tanh(x)$? – mrsquee Jan 01 '21 at 17:50

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