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Evaluate log10x
Evaluate log2x
Evaluate lognx
Evaluate n-th power
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Natural logarithm calculator

- By Dr. Minas E. Lemonis, PhD - Updated: March 3, 2019

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.

loge-graph

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:

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

See also
Evaluate log10x
Evaluate log2x
Evaluate lognx
Evaluate n-th power
All evaluation tools