Documentation/Calc Functions/LN

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This page is a translated version of the page Documentation/Calc Functions/LN and the translation is 48% complete.
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Funktionsnavn:

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(tal)

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:

Formlen for LN-funktionen er:

  • 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.

GIFen herunder illustrerer funktionen LN.

LN function

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(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

Beslægtede LibreOffice-funktioner:

EKSP

LOG

LOG10

POTENS

ODF standard:

Tilsvarende Excel-funktioner:

LN