IMLOG10 Google Sheet Formula

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IMLOG10 Formula Syntax

=IMLOG10("3+4i")

Example Use Case

Calculating the base-10 logarithm of a complex number

Understanding the IMLOG10 Formula

The IMLOG10 function in Excel returns the base-10 logarithm of a complex number. It's an advanced mathematical tool for complex analysis—like solving exponential equations with complex terms or analyzing data on a logarithmic scale with complex inputs.

IMLOG10("3+4i") returns the base-10 logarithm of the complex number "3+4i". It takes a complex number argument in the form of text ("x+yi" or "x+yj"), calculating log₁₀(z) = log₁₀|z| + i×Arg(z)/ln(10)—useful for applications in engineering, physics, or mathematics requiring base-10 complex logarithms.

Why Use IMLOG10?

IMLOG10 enables complex logarithmic calculations in base 10—think decibel calculations or scaling in complex domains. Its implementation of the complex common logarithm makes it valuable for fields that traditionally use base-10 scales but must extend to complex values.

Example with Sample Data

Complex NumberFormulaResult
"3+4i"=IMLOG10("3+4i")0.6989700043+0.4027191962i
"1+i"=IMLOG10("1+i")0.1505149978+0.3410940884i
"100"=IMLOG10("100")2

IMLOG10 calculates base-10 logarithms: log₁₀(3+4i) approximately equals 0.70+0.40i. For real positive numbers like 100, it works exactly like the regular LOG10 function, returning 2. It's a complex base-10 logarithm calculator.

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