The Logarithm of a number, to a given base, is the power to which the base must be raised to give that number.
Therefore,
The Excel LOG function calculates the logarithm of a given number, to a supplied base.
The format of the function is :
where the arguments are listed in the table below :
number    The positive real number to calculate the logarithm of 
[base]   
An optional argument that specifies the base to which the logarithm should be calculated If omitted, the [base] argument takes the value 10 (i.e. the logarithm to the base 10 is calculated) 
In the example below, the Excel Log function is used to calculate the logarithms of different numbers, using different bases.
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:

Note that, in cells A2 and A4 of the above spreadsheet, the [Base] argument has not been supplied to the function and so, in these examples, base 10 is used.
Further examples of the Excel Log function can be found on the Microsoft Office website.
If you get an error from your Excel Log function, use the following table to diagnose the likely cause :
#NUM!    Produced if either the supplied number argument or the supplied [base] argument is negative or zero 
#DIV/0!    Produced if the supplied [base] argument is equal to 1 
#NAME?    Produced if the supplied number argument or the supplied [base] argument is not a numeric value 