IMLOG10 Function (LibreOffice Calc)

IMLOG10 finds the base-10 logarithm of a complex number. Unlike the ordinary real-valued LOG10, it accepts a complex-number text representation and returns a complex result as text. You can use it to analyse magnitude and phase in one formula. For nonzero z, the underlying mathematical relationship is log10(z) = ln(z)/ln(10) using the selected complex logarithm branch.

=IMLOG10("3+4i")

Expected mathematically and observed in native Calc 25.2.3.2: 0.698970004336019+0.402719196273373i. The real coefficient is log10(5) because |3+4i|=5; the imaginary coefficient is the argument in radians divided by ln(10).

=IMLOG10(ComplexNumber)

ComplexNumber — Required. One complex string such as "3+4i", "1+j", a cell reference to complex text, output from COMPLEX, or a real numeric value such as 10.

There is one required argument, and no optional base: it is always 10. The i or j suffix denotes the imaginary unit, not a separate field. An input such as COMPLEX(3;4) has two internal arguments separated by a semicolon in standard English Calc syntax; other locales or customized settings may use different separators or numeric punctuation. Official online Help displayed 26.8 Help on 2026-10-11; these examples were actually executed in Calc 25.2.3.2. No first-version or universal platform support is inferred.

Enter these sample values in a blank sheet:

On a narrow screen, scroll this table sideways to see every column.

In D3 enter:

=IMLOG10(A3)

Expected / observed: 0.698970004336019+0.402719196273373i. For A2, the formula =IMLOG10(A2) returns 0.150514997831991+0.34109408846046i. These values are complex text, even though their real coefficients look like ordinary decimals.

For a real positive value:

=IMLOG10(100)

Expected / observed: the text 2 (=ISTEXT(IMLOG10(10)) returned TRUE in native Calc). If the data are guaranteed positive real numbers and you need ordinary numeric output, use LOG10(100) instead.

The following uses B2 and C2 to build the same 3+4i input:

=IMLOG10(COMPLEX(B2;C2))

Expected / observed: 0.698970004336019+0.402719196273373i.

To extract a numeric base-10 log of the magnitude from the result, use:

=IMREAL(IMLOG10("3+4i"))

Expected / observed in native Calc: 0.698970004336019 as a numeric real component. This expression was executed separately; the evidence file records the exact formula and result.

An exact, natively tested real-number round trip is:

=IMPOWER(10;IMREAL(IMLOG10("100")))

Expected / observed: 100. It is intended as a consistency example, not an efficient substitute for POWER(10;2).

• Undefined at zero: =IMLOG10(0) returned Err:502 in native Calc 25.2.3.2. No complex logarithm exists for zero; don’t replace zero with a small number without a stated calculation rule.
• Malformed imported text: =IMLOG10("wrong") returned Err:502 (code 502). Confirm the cell is complex text in supported notation instead of a heading or unrecognized suffix.
• LOG10 versus IMLOG10: LOG10 handles positive real numbers and returns a number; IMLOG10 handles complex strings and returns a complex string. For real input =IMLOG10(10) displayed text 1 in native testing.
• Precision/formatting: Some outputs have long decimal components. They are text; converting via VALUE on the whole string is not correct. Use IMREAL or IMAGINARY on the complex string to work with components numerically.
• Phase and branch: As with any complex logarithm, the imaginary part reflects a chosen argument branch. For measurements near a branch boundary, consider how you will unwrap phase rather than blindly comparing strings.
• j representation: =IMLOG10("1+j") natively returned 0.150514997831991+0.34109408846046j. This is equivalent in mathematical value to the i representation above.

Microsoft’s official Excel IMLOG10 help also describes a one-argument complex base-10 logarithm. Excel compatibility here is documentation-checked only; no Excel workbook tests were run, and formula separator/display differences can matter after import. ODF nomenclature and mobile/web support were not tested.

Confirmed as file paths in the 2026-10-10 owner source archive only: IMLN, IMLOG2, IMPOWER, COMPLEX, IMREAL, IMARGUMENT, and LOG10.

1. LibreOffice 26.8 Help — IMLOG10, checked 2026-10-11: states the base-10 complex-log purpose, the one-argument syntax, text representation, and rounded 1+j example.
2. LibreOffice Analysis Functions Help index, checked 2026-10-11: function family and input syntax conventions.
3. Microsoft Excel IMLOG10 documentation, checked 2026-10-11, comparison only.
4. Original general LibreOffice Calc Help link, general help index.

Selected example formulas were run in LibreOffice Calc 25.2.3.2 on Linux on October 12, 2026. The official Help may cover a newer version. Tests of selected formulas do not certify every locale, interactive array operation or file round trip. View the example-check record.

Official IMLOG10 reference · Editorial standards