===== Natural logarithm of real numbers =====
==== Function ====
| @#FFBB00: definiendum | @#FFBB00: $\mathrm{ln}:\mathbb R_+^*\to \mathbb R$ |
| @#55EE55: postulate   | @#55EE55: $\mathrm{ln}=\mathrm{exp}^{-1}$ |

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

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

<code>
Log[a] == Log[b] + Integrate[1/(t+b)-1/(t+a),{t,0,Infinity}]
</code>

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

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=== Subset of ===
[[Real logarithm]], [[Natural logarithm of complex numbers]]
=== Context ===
[[Exponential function]], [[Inverse function]]