## 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.