Documentation/Calc Functions/LN
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LN
Kategori:
Matematisk
Resume:
Returnerer den naturlige logaritme af et tal baseret på konstanten e. Konstanten e har en værdi på tilnærmelsesvis 2,71828182845904.
Syntaks:
LN(Number)
Returnerer:
Returnerer et naturligt tal.
Argumenter:
Tallet er det reelle tal eller en reference til en celle, der indeholder det tal, hvis naturlige logaritme skal beregnes.
Hvis tallet er negativt eller 0, så returnerer funktionen en fejlværdi.
Yderligere oplysninger:
- 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.
Eksempler:
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(EKSP(1)) | Here the function returns the natural logarithm of the constant e. | 1 |
=LN(EKSP(345)) | Here the function returns the natural logarithm of e raised to the power of 345, which is 345. | 345 |
=EKSP(LN(789)) | Here the function returns e raised to the power of the natural logarithm of 789, which is 789. | 789 |
Beslægtede LibreOffice-funktioner:
ODF standard:
Tilsvarende Excel-funktioner:
LN