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 syntax of the function is:
where the arguments are as follows:
number    The positive real number that you want 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 uses the default value 10 (i.e. the logarithm to the base 10 is calculated). 
The following spreadsheet shows four examples of the Excel Log function:
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 cases, base 10 is used.
Further examples of the Excel Log function are provided on the Microsoft Office website.
If you get an error from the Excel Log function, this is likely to be one of the following:
#NUM!    Occurs if either the supplied number argument or the supplied [base] argument is negative or zero. 
#DIV/0!    Occurs if the supplied [base] argument is equal to 1. 
#VALUE!    Occurs if the supplied number argument or the supplied [base] argument is nonnumeric. 