# The Excel LOG Function

Related Function:
LN Function
Logarithm

The Logarithm of a number, to a given base, is the power to which the base must be raised to give that number.

Therefore,

If   ax = b   Then   Lna(b) = x

## Function Description

The Excel LOG function calculates the logarithm of a given number, to a supplied base.

The syntax of the function is:

LOG( number, [base] )

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).

## Excel Log Function Examples

The following spreadsheet shows four examples of the Excel Log function:

Formulas:
A
1 =LOG( 64, 2 )
2 =LOG( 100 )
3 =LOG( 4, 0.5 )
4 =LOG( 500 )
Results:
A B
1 6   26 = 64; Therefore, Log2(64) = 6
2 2   102 = 100; Therefore, Log10(100) = 2
3 -2   0.5-2 = 4; Therefore, Log0.5(4) = -2
4 2.698970004   102.698970004 = 500; Therefore, Log10(500) = 2.698970004

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.

For further examples of the Excel Log function, see the Microsoft Office website.

## Log Function Errors

If you get an error from the Excel Log function, this is likely to be one of the following:

Common Errors
 #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 non-numeric.