# Documentation/Calc Functions/LN

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## Function name:

LN

## Category:

Mathematical

## Summary:

Calculates the logarithm to the base *e* or natural logarithm of a positive real number. *e* is a mathematical constant known as Euler's number, which has a value of approximately 2.71828182845904. The natural logarithm of *x* is often written as ln(*x*) or log_{e}(*x*).

## Syntax:

LN(**Number**)

## Returns:

Returns a real number that is the natural logarithm of the specified number.

## Arguments:

**Number** is a positive real number, or a reference to a cell containing that number, that is the value for which the natural logarithm is to be calculated.

- If
**Number**is non-numeric, then LN reports a #VALUE! error. - If
**Number**is less than or equal to 0, then LN reports an invalid argument error (Err:502).

## Additional details:

- For any positive real number
*x*, [math]\displaystyle{ e^{\text{ln}(x)}=x }[/math] and [math]\displaystyle{ \text {ln}(e^x)=x }[/math]. - A series expansion for the natural logarithm of the positive real number
*x*is:

[math]\displaystyle{ \text{ln}(x)~=~2 \left(\left(\frac{x-1}{x+1}\right)+\frac{1}{3} \left(\frac{x-1}{x+1}\right)^3 +\frac{1}{5} \left(\frac{x-1}{x+1}\right)^5+...\right) }[/math]

- To convert the natural logarithm of a positive real number
*x*to a common logarithm (base-10), use the formula [math]\displaystyle{ \text{log}(x)=\text{ln}(x)~/~\text{ln}(10) }[/math]. - Additional information about natural logarithms can be found at Wikipedia's Natural logarithm page.
- The figure below illustrates the LN function.

## Examples:

Formula | Description | Returns |
---|---|---|

=LN(3.5) | Here the function returns the natural logarithm of 3.5. | 1.25276296849537 |

=LN(0.5) | Here the function returns the natural logarithm of 0.5. | −0.693147180559945 |

=LN(D1) where cell D1 contains the value 1. | Here the function returns the natural logarithm of 1. | 0 |

=LN(EXP(1)) | Here the function returns the natural logarithm of the constant e. |
1 |

=LN(EXP(345)) | Here the function returns the natural logarithm of e raised to the power of 345, which is 345. |
345 |

=EXP(LN(789)) | Here the function returns e raised to the power of the natural logarithm of 789, which is 789. |
789 |

## Related LibreOffice functions:

## ODF standard:

## Related (or similar) Excel functions:

LN