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LN

LN

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Description 

Use this function to return the natural logarithm of a given number. Supported in Chains. 

The natural logarithm is equivalent to log base e of a number, where e is Euler's number, a mathematical constant with an approximate value of 2.71828182845904. 

This function models exponential decay and the output of the function at a given point is inversely proportional to the rate of change of the function at that point. Generally, this function is used in applications relating to compound interest.

The function that is the inverse of the logarithm function is the  EXP (exponential) function, which represents exponential growth.

 

Syntax

LN(number)

 

Inputs

This function has the following arguments:

Name Required Description Valid input
number Yes The number to be acted on.  A cell reference, a number, or a formula which results in either of these.  It must be a positive value.

 

Example

Sample formulas

Sample data

  A B
1 4 1
2 35 11
3 12 54

Sample formulas

Use case Formula Explanation and Result
Calculate the natural logarithm of a number in a cell. =LN(A1)

This formula works in the following manner:

  • LN(: This is the function itself, which returns the natural logarithm of a number.
  • A1: The number argument, referencing A1 (which contains 4).

For this data set, this formula returns 1.386294361.
Calculate the natural logarithm of Euler's number (e). =LN(EXP(1))

This formula works in the following manner:

  • EXP(1): This inner function returns Euler's number (e), approximately 2.718.
  • LN(...): The outer function calculates the natural logarithm of the result from EXP(1). The natural log is the inverse of the exponential function, so LN(e) equals 1.

This formula returns 1.
Calculate the natural logarithm of a calculated value. =LN(B3-A3)

This formula works in the following manner:

  • B3-A3: The inner expression is calculated first (54 - 12), resulting in 42.
  • LN(42): The function takes the result (42) as its number argument.

For this data set, this formula returns 3.737669618.
Show an error for a negative number. =LN(B2-A2)

This formula works in the following manner:

  • B2-A2: The inner expression is calculated first (11 - 35), resulting in -24.
  • LN(-24): The function attempts to calculate the natural logarithm of a negative number, which is undefined.

For this data set, this formula returns #NUM!.

 

Notes

  • Wildcards don't work with this function. 
  • Because logarithms can't be evaluated for non-positive numbers,  =LN(0) returns a #NUM! error, as does any case where the supplied number is negative.

 

Related functions

ABS
EXP
MOD
N
POWER
PRODUCT
SIGN
SQRT
SUBTOTAL
SUM
SUMIF
SUMIFS
SUMPRODUCT

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Description Use this function to return the natural logarithm of a given number. Supported in Chains. The natural log...