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 syntax of the function is:
where the number argument is the positive real number that you want to calculate the natural logarithm of.
In the example spreadsheet below, the Excel Ln function is used to calculate the natural logarithms of three different numbers, 1, 100 and 0.5:
Formulas:

Results:

For further examples of the Excel Ln function, see the Microsoft Office website.
If you get an error from the Excel Ln function, this is likely to be one of the following:
#NUM!    Occurs if the supplied number argument is negative or zero. 
#VALUE!    Occurs if the supplied number argument is nonnumeric. 