IMLOG10 Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this identifies a verified release, not a final supported version.
• Scope: Desktop Calc with its Analysis add-in, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight reference formulas and the listed diagnostics were recalculated after XLSX import in 4.1.16 on Linux x86-64, Build 9816. Source and independent reference calculations were also checked.

IMLOG10 returns the selected complex logarithm to base 10. It is the principal natural logarithm divided by ln(10), so both the real and imaginary components are scaled. It is not merely LOG10 of the input magnitude with the phase discarded. Release entry.

=IMLOG10(ComplexNumber)

Exactly one nonzero complex-number argument is required. The parser recognizes lowercase i/j forms and pure real forms. Zero and invalid complex text are rejected. The operation inherits its principal phase convention from the natural-log helper.

The native column records the saved 4.1.16 results. The native strings are retained exactly. Independent component references are rounded to twelve decimal places, with rounded negative zero shown as zero. A tiny stored residual can therefore appear in the native string beside a reference component rounded to zero. Every successful result below is string-typed, including pure real-looking outputs.

For 3+4i, the real component of =IMLOG10("3+4i") is log10(5)≈0.698970004336. The imaginary component is arg(3+4i)/ln(10)≈0.402719196273. It is a scaled radian phase, not an unscaled angle in degrees.

A cell formula =IMLOG10(A2) uses the complex value in A2. When interpreting the real component as a logarithmic magnitude, apply any domain-specific amplitude or power factor separately. The function alone does not choose a decibel convention.

The implementation first calculates the principal natural logarithm and multiplies by a stored approximation to 1/ln(10). That explains the relationship to IMLN without promising bit-for-bit equality for every separately rounded composition.

On the negative real axis, log10(−1)=iπ/ln(10), approximately 1.364376353842i. On the unit circle the real component is zero because the magnitude is 1.

Multiplying the result by ln(10) and then applying the complex exponential recovers the original nonzero value mathematically. However, the principal-log product rule can differ by multiples of 2πi/ln(10). Branch information must be retained when simplifying complex expressions.

Zero is rejected by the inherited logarithm guard. Invalid text is also rejected. The tested negative-zero-looking input has selected phase +π on the negative real axis, as shown below.

A small real component can be legitimate when the input magnitude is close to 1. Display rounding may hide it, and a principal phase can jump across the negative real axis. Neither effect should be interpreted as a base-conversion failure without checking the actual components.

These additional formulas were recalculated through the same import path. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

The IMLOG10 guide for Calligra Sheets documents that product’s own syntax and tested behavior. A shared function name does not guarantee the same argument conversion, text parsing, branch or precision rules.

• Function-specific release entry
• Complex algorithm or collection helper
• Strict complex-string parser
• Finite-output string formatter
• Inherited principal natural-log operation

The saved ODS retained every tested formula identity. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence covers the eight reference formulas and listed diagnostics only. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.