The Logarithm of a number, to a given base, is the power to which the base must be raised to give that number.
The Natural Logarithm of a number, (generally written as Ln(x) or Log_{e}(x) ), is the logarithm to the base e.
Therefore,
The Excel LN function calculates the natural logarithm of a given number.
The format of the function is :
where the number argument is a positive real number that you want to calculate the natural logarithm of.
In the example below, the Excel Ln function is used to calculate the natural logarithms of different numbers.
The format of the functions is shown in the spreadsheet on the left and the result is shown in the spreadsheet on the right.
Formulas:

Results:

Further examples of the Excel Ln function can be found on the Microsoft Office website.
If you get an error from your Excel Ln function, use the following table to diagnose the likely cause :
#NUM!    Produced if the supplied number argument is negative or zero 
#NAME?    Produced if the supplied number argument is not a numeric value 