Purpose
Return value
Syntax
=IMLOG10(complex_num)- complex_num - The complex number in the form "x+yi".
How to use
The Excel IMLOG10 function returns the base-10 logarithm of a complex number. For example, given the number "0-100i" as input, the function returns "2-0.682188176920921i" as output.
=IMLOG10("0-100i") // returns 2 - 0.682188176920921i
The real part of the output is equal to the logarithm (base 10) of the complex number's magnitude.
=LOG10(IMABS("0-100i")) // returns 2
The imaginary part of the output is equal to the angle (in radians) of the complex number divided by the natural logarithm of 10.
=IMARGUMENT("0-100i")/LN(10) // returns -0.682188177
Explanation
In math, the complex logarithm of any base can be described in terms of the natural logarithm using the change of base formula.
In Excel, we can define the base-10 logarithm using the following formula.
=IMDIV(IMLN("x+yi"),IMLN("10"))
See the IMLN function for a more in-depth explanation of the complex logarithm.
Related functions
COMPLEX Function
The Excel COMPLEX function creates a complex number with given real and imaginary coefficients. COMPLEX returns a text result in the form x + yi or x + yj....
IMLN Function
The Excel IMLN function returns the natural logarithm of a complex number.
IMLOG2 Function
The Excel IMLOG2 function returns the base-2 logarithm of a complex number.
LOG10 Function
The Excel LOG10 function returns the base 10 logarithm of a number. For example, LOG10(100) returns 2, and LOG10(1000) returns 3.
