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#Engineering

IMLOG10

Excel Functions

Returns the base-10 logarithm of a complex number.

Syntax

EXCEL 
=IMLOG10(complex_num)

Arguments

Parameter Description
complex_num The complex number in the form "x+yi".

Return Value

The logarithm of the complex number.

Details

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. The real part of the output is equal to the logarithm (base 10) of the complex number's magnitude. The imaginary part of the output is equal to the angle (in radians) of the complex number divided by the natural logarithm of 10. 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.

Examples

Example 1

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

EXCEL 
=IMLOG10("0-100i") // returns 2 - 0.682188176920921i
Example 2

The real part of the output is equal to the logarithm (base 10) of the complex number's magnitude.

EXCEL 
=LOG10(IMABS("0-100i")) // returns 2
Example 3

The imaginary part of the output is equal to the angle (in radians) of the complex number divided by the natural logarithm of 10.

EXCEL 
=IMARGUMENT("0-100i")/LN(10) // returns -0.682188177
Explanation

In Excel, we can define the base-10 logarithm using the following formula.

EXCEL 
=IMDIV(IMLN("x+yi"),IMLN("10"))

See Also

COMPLEX IMLN IMLOG2 LOG10