Natural Logarithm (ln₍x₎) ○◂｜appendage｜___｜20260628174208-01-•

Natural logarithm	…
Graph of part of the natural logarithm function. The function slowly grows to positive infinity as x increases, and slowly goes to negative infinity as x approaches 0 (“slowly” as compared to any power law of x).	…
General information	…
General definition	$\ln x={\log }_{e}x$
Motivation of invention	hyperbola quadrature
Fields of application	Pure and applied mathematics
Domain, codomain and image	…
Domain	${\mathbb{R}}_{>0}$
Codomain	$\mathbb{R}$
Image	$\mathbb{R}$
Specific values	…
Value at +∞	+∞
Value at e	1
Value at 1	0
Value at 0	−∞
Specific features	…
Asymptote	$x=0$
Root	1
Inverse	$\exp x$
Derivative	$\frac{d}{dx}\ln x=\frac{1}{x},x>0$
Antiderivative	$\int \ln xdx=x\left(\ln x-1\right)+C$

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