Math Natural exponential function Natural logarithm function

Natural logarithm function

The inverse function of the natural exponential function is the natural logarithm function or ln-function:



The ln-functionis a logarithmic function with the Euler number as a basis:



The natural logarithm short $\ln$ is a logarithm with base $e$:


Since the natural logarithm function is the inverse function of the exponential function with base e, the following computation law applies:

$x=\ln(e^x)$ $=e^{\ln(x)}$

Tip: The rule is advantageous in deriving the derivative of general exponential functions.