Natural logarithm of real numbers

Function

definiendum $\mathrm{ln}:\mathbb R_+^*\to \mathbb R$
postulate $\mathrm{ln}=\mathrm{exp}^{-1}$

$\int_1^y \frac {1 } {x} {\mathrm d}x = \ln(y) $

$\int_0^{y} \frac {1 } {1+x } {\mathrm d}x = \ln(1+y) $

The function $x\mapsto\frac{x}{x-1}\log(x)$ is one without bad behaviours (singularities) on $[0,\infty)$.


Subset of

Context

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