# The Excel IMLOG10 Function

Related Function:
IMLN Function
Common Logarithm of a Complex Number

The common (base 10) logarithm of a complex number is calculated by the equation:

See Wikipedia for further information on complex numbers.

## Function Description

The Excel Imlog10 function returns the common (base 10) logarithm of a supplied complex number.

The syntax of the function is:

IMLOG10( inumber )

where the inumber argument is the complex number that you want to find the base 10 logarithm of.

### Complex Numbers in Excel

Note that complex numbers are simply stored as text in Excel. When a text string in the format "a+bi" or "a+bj" is supplied to one of Excel's built-in complex number functions, this is interpreted as a complex number.

Also the complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.

Therefore, the inumber argument can be supplied to the Excel Imlog10 function as any of the following:

• A simple number;
• A complex number encased in quotation marks - e.g. "5+3i";
• A reference to a cell containing a complex number or a numeric value;
• A value returned from another Excel function or formula.

## Imlog10 Function Examples

The spreadsheets below show four examples of the Imlog10 function:

Formulas:
A B
1   =IMLOG10( 2 )
2   =IMLOG10( "1-2i" )
3 2.5-i =IMLOG10( A3 )
4   =IMLOG10( COMPLEX( 1, -1 ) )
Results:
A B
1   0.301029995663981
2   0.349485002168009-0.480828578784234i
3 2.5-i 0.349485002168009-0.201359598136687i
4   0.150514997831991-0.34109408846046i

Note that, in the above example spreadsheet:

• The integer 2, used in cell B1, is equal to the complex number 2+0i;
• The example in cell B4 uses the Excel Complex Function to create the complex number 1-i.

Further details and examples of the Excel Imlog10 function are provided on the Microsoft Office website

## Imlog10 Function Errors

If you get an error from the Excel Imlog10 Function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if the supplied inumber argument is not recognised as a complex number. #VALUE! - Occurs if the supplied inumber argument is a logical value.