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 loge(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