Natural logarithm function
The inverse function of the natural exponential function is the natural logarithm function or ln-function:
$f(x)=\ln(x)$
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Remember
The ln-functionis a logarithmic function with the Euler number as a basis:
$\ln(x)=\log_e(x)$
$\ln(x)=\log_e(x)$
![](https://math.lakschool.com/en/themen/e_funktion/images/ln_funktion.png)
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Remember
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.
$x=\ln(e^x)$ $=e^{\ln(x)}$
Tip: The rule is advantageous in deriving the derivative of general exponential functions.