Documentation/Calc Functions/LN/en

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, $$e^{\text{ln}(x)}=x$$ and $$\text {ln}(e^x)=x$$.


 * A series expansion for the natural logarithm of the positive real number x is:

$$\text{ln}(x)~=~2 \left(\left(\frac{x-1}{x+1}\right)+\frac{1}{3} \left(\frac{x-1}{x+1}\right)^3 +\frac{1}{5} \left(\frac{x-1}{x+1}\right)^5+...\right)$$


 * To convert the natural logarithm of a positive real number x to a common logarithm (base-10), use the formula $$\text{log}(x)=\text{ln}(x)~/~\text{ln}(10)$$.


 * Additional information about natural logarithms can be found at Wikipedia's Natural logarithm page.


 * The figure below illustrates the LN function.

Related LibreOffice functions:
EXP

LOG

LOG10

POWER

ODF standard:
Section 6.16.39, part 2

Equivalent Excel functions:
LN