Extra explanation: natural logarithm | Wiskunde op Tilburg University

Introduction 1: There exists a special exponential function:

$y(x)=e^x$ , with

$e$ (

$\approx 2.718$ ). (See Exponential functions Extra explanation: base e.)

Introduction 2: The logarithmic function (See Logarithmic functions Extra explanation: natural logarithm) with base

$e$ is called the natural logarithm and denoted as

$y(x)=\ln x$ .

Theorem:

$y = \ln e^y$ ,
$x = e^{\ln x}$ , $x>0$ .