How to use the LN function
What is the LN function?
The LN function calculates the natural logarithm of a number.
What is ln?
Ln is an abbreviation of natural logarithm are based on the constant e. It is the inverse of the exponential function.
The natural logarithm, or log base e, is defined using the following limit:
ln(x) = lim (n->infinity) (x(1/n) - 1) * n
Some key properties of the natural logarithm:
- The natural log of 1 is 0.
- LN is undefined for negative numbers.
- LN is the inverse of the EXP function
LN(EXP(x)) = x.
What is e?
It is the base of the natural logarithm, ln. e is defined to be the limit of (1 + 1/n) raised to the nth power as n approaches infinity.
In equation form: e = lim (1 + 1/n)n as n -> infinity
The limit of this exponential growth pattern is the unique number e. For example:
(1 + 1/1)1Â = 2
(1 + 1/2)2Â = 2.25
(1 + 1/3)3Â = 2.37037
The limit of this exponential growth pattern is the unique number e.
e = e1Â equals 2.71828182845904.
e2Â equals 7.389056099
What are the other logarithmic functions in Excel?
| Excel function | Description |
|---|---|
| LOG | Returns the logarithm with a given base. |
| LN | Returns the natural logarithm (base e) of a number |
| LOG10 | Returns the base-10 logarithm of a number |
| LOG2 | Returns the base-2 logarithm of a number |
What applications does the natural logarithm have?
Natural logs have applications in math, science, and finance for calculating compound growth, diffusion, acidity, and more. LN is useful whenever natural exponential growth or decay is involved.
Formula in cell C3:
Excel Function Syntax
LN(number)
Arguments
| number | Required. The positive numerical value for which you want the natural logarithm. |
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Functions in 'Math and trigonometry' category
The LN function function is one of many functions in the 'Math and trigonometry' category.
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