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## Natural logarithm calculator

This tool evaluates the natural logarithm of a number: $$\ln{x}$$. Enter the argument x below.

 x = Result: $$\ln {x}$$ =
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## Definitions

### General

The natural logarithm of a number x, is a power p so that ep = x, where e is a mathematical constant, approximately equal to 2.718. In modern notation natural logarithm is written as $$\ln{x}$$ or $$\log_{e}{x}$$. Any positive real number has a natural logarithm. The natural logarithm of 1 is 0, while the natural logarithm of 0 approaches negative infinity.

The graph of the natural logarithm function is shown in the figure below. It is a monotonic function.

### Properties

The derivative of the natural logarithm function is:

$\left(\ln x\right)' = \frac{1}{x}$

The integral of the natural logarithm function is given by:

$\int \ln x\, \mathrm{d}x = x\ln{x}-x +C$