IMLOG10 in Google Sheets: Use One Argument for Complex Decimal Logs

• Introduced: first introduction date is not established by the reviewed official history; no desktop release number is inferred.
• Availability: documented in the rolling Google Sheets service; these examples use the web worksheet workflow.
• Checked: October 14, 2026; official IMLOG10 reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=IMLOG10(value)

Google permits ordinary real numbers and quoted complex values. It explicitly equates IMLOG10 with the general IMLOG function when the latter’s base is ten.

The page’s sample-formula list adds extra base-like arguments, but its signature and every calculated example use only value. This guide follows the coherent one-argument contract. The extra sample arguments are not evidence of an optional base parameter.

Changing to another logarithm base requires the appropriate function or explicit base conversion. IMLOG2 has fixed base two; it is not an alternate spelling with the same numerical result.

Enter the first column as Plain text in A2:A4. Put =IMLOG10(A2) in B2 and fill down. Extract real and imaginary coefficients into C and D.

The magnitudes are five, ten and one hundred. Their base-ten logarithms are approximately 0.698970004, one and two. All three values point in the same first-quadrant direction.

The imaginary coefficient equals that radian angle divided by LN(10). It is not the angle itself or a degree display.

Use =IMREAL(B2) and =IMAGINARY(B2) to inspect numeric components. The shown decimals are independent rounded expectations, not exact native output strings.

Google explicitly documents =IMLOG10(100) returning two. For the complex input 60+80i, the real logarithm coefficient is also two because the magnitude is one hundred, but the imaginary coefficient is nonzero.

A report that keeps only the real component cannot distinguish those different directions. Ordinary numeric one hundred lies on the positive real axis, whereas 60+80i does not.

A direct source control is =IMLOG10("1+i"), with coefficients approximately 0.150514998 and 0.341094088. The magnitude is SQRT(2), so the real component is half LOG10(2).

For each primary input, compare with a constructed result using IMLN:

=COMPLEX(IMREAL(IMLN(A2))/LN(10),IMAGINARY(IMLN(A2))/LN(10))

The independent expected coefficients match B2:B4. Both natural-log coefficients must be divided by LN(10); scaling only the real one changes the intended result.

For 3+4i, the natural-log components are approximately 1.609437912 and 0.927295218. Division by approximately 2.302585093 yields the first row.

The IMLN reference contains a displayed-equation omission, discussed in its guide. This calculation uses the corrected model consistent with its worked outputs, rather than copying that incomplete equation.

The difference between the last two logarithms is one with zero imaginary coefficient:

=IMSUB(IMLOG10("60+80i"),IMLOG10("6+8i"))

It represents a tenfold magnitude increase with unchanged direction. The difference between the second and first has real coefficient LOG10(2), approximately 0.301029996, and imaginary coefficient zero.

These controls distinguish doubling from increasing by one decimal order of magnitude. An additive change in the logarithm represents a multiplicative scale change in the original quantity.

Only positive-real scaling is used. Arbitrary complex products can involve angle changes and branch choices that this example does not resolve.

For B2, enter:

=IMEXP(COMPLEX(IMREAL(B2)*LN(10),IMAGINARY(B2)*LN(10)))

The expected reconstructed quantity is 3+4i. Filling the equivalent formula down reconstructs 6+8i and 60+80i.

IMEXP receives a natural complex exponent after the base scaling is reversed. Retain both components and unrounded cell results when evaluating recovery.

For this fixture, compare each coordinate against the original with an explicit tolerance such as 0.00000001. A larger tolerance than a very small unit-scale example reflects the larger final coordinates; it is a chosen check, not a documented service guarantee.

The logarithm of zero is mathematically undefined. The dedicated reference does not specify a complete error table or global branch interval, so no native zero code or negative-axis endpoint is assigned here.

All new complex-log outputs stay in the first quadrant, with separate numeric controls directly supported by Google. The one-argument contract resolves the source’s inconsistent samples without inventing a second optional parameter. No native Sheets execution was performed.

• Google IMLOG10 reference.
• Editorial testing standards.

Examples use fictional data, English function names and comma separators. Expected outputs are independent mathematical calculations or explicitly documented rules, not native Sheets captures. Check the spreadsheet locale when reproducing punctuation-sensitive formulas.