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