# Documentation/Calc Functions/LN

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LN

Matematisk

## Resume:

Returnerer den naturlige logaritme af et tal baseret på konstanten e. Konstanten e har en værdi på tilnærmelsesvis 2,71828182845904.

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.
• If Number is less than or equal to 0, then LN reports an invalid argument error (Fejl:502).

## Yderligere oplysninger:

• For any positive real number x, $\displaystyle{ e^{\text{ln}(x)}=x }$ and $\displaystyle{ \text {ln}(e^x)=x }$.
• A series expansion for the natural logarithm of the positive real number x is:

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

• To convert the natural logarithm of a positive real number x to a common logarithm (base-10), use the formula $\displaystyle{ \text{log}(x)=\text{ln}(x)~/~\text{ln}(10) }$.
• Additional information about natural logarithms can be found at Wikipedia's Natural logarithm page.
• GIFen herunder illustrerer funktionen LN.
LN function
LN function

## Eksempler:

Formel Beskrivelse 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

LN