#type/note

Logistic function

l(x)=ln⁡(x)l2(x)=ln⁡(1−x)

Such that:

limx→0l(x)=−∞limx→1l(x)=0limx→0l2(x)=0limx→1l(x)=−∞

where, for both:

l(0.5)=l2(0.5)=−ln⁡(2)
top=0.5; bottom=-10.5
left=-1; right=2
---
y=\ln{x}
y=\ln{(1-x)}
y=-\ln{2}
limx→0xln⁡(x)=0limx→1xln⁡(x)=0limx→0(1−x)ln⁡(1−x)=0limx→1(1−x)ln⁡(1−x)=0limx→0(1−x)ln⁡(x)=−∞limx→1(1−x)ln⁡(x)=0limx→0xln⁡(1−x)=0limx→1xln⁡(1−x)=−∞
top=0.5; bottom=-2.5
left=-0.5; right=1.5
---
y=x\ln(x)
y = (1-x)\ln(1-x)
y=(1-x)\ln(x)
y=x\ln(1-x)

def l(x):
	return np.log(x)

def l2(x):
	return np.log(1-x)