> For the complete documentation index, see [llms.txt](https://sisyphus.gitbook.io/project/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://sisyphus.gitbook.io/project/machine-learning/logistic-regression/logistic-function.md).

# Logistic Function

A **logistic function** or **logistic curve** is a common "S" shape ([sigmoid curve](https://en.wikipedia.org/wiki/Sigmoid_function)), with equation:

&#x20;                                                 <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f42e36c949c94189976ae00853af9a1b618e099" alt="{\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}}" data-size="original">

where

* e = the [natural logarithm](https://en.wikipedia.org/wiki/Natural_logarithm) base (also known as [Euler's number](https://en.wikipedia.org/wiki/E_\(mathematical_constant\))),
* x0 = the x-value of the sigmoid's midpoint,
* L = the curve's maximum value, and
* k = the steepness of the curve.

&#x20;                                 <img src="https://443921002-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGHUhl6VYqrZm4Re77O%2F-LOBduJI0U3ErwK9tLHD%2F-LOBiefxMZ86TONKvtbu%2FScreen%20Shot%202018-10-06%20at%209.12.20%20PM.png?alt=media&amp;token=3e6ab284-7904-404d-ae71-ff8fa72cf725" alt="" data-size="original">

![](https://wikimedia.org/api/rest_v1/media/math/render/svg/c9ccf5c48fc073952bbbafe5e2a11d4eaddb90cb)