LOG2 Function (Gnumeric)

• Introduced: First release not established.
• Supported in: Gnumeric 1.12.62, with no retirement established.
• Scope: Desktop Gnumeric with the Mathematics plugin; English comma-separated formulas are shown.
• Checked: October 14, 2026. Reference and boundary tables plus the explicit advanced-check formula were recalculated through 1.12.57 ssconvert. Current 1.12.62 source was inspected; that later release was not executed.

LOG2 returns the base-two logarithm of a positive number: the exponent y such that 2^y=x. It is useful for multiplicative scales and powers of two. The result need not be an integer, and values between 0 and 1 have negative logarithms. Versioned function help.

=LOG2(x)

Exactly one numeric x is required, and x must be strictly positive. Zero and negative inputs are explicitly rejected with #NUM!. LOG2 is not a binary-string decoder: quoted digits representing another number system must be converted under that system’s rules first. Function implementation.

Ordinary results are rounded to twelve decimal places; tiny nonzero values use scientific notation. The eight reference rows were independently checked.

The examples show LOG2(8)=3 and LOG2(1024)=10 because 8=2^3 and 1024=2^10. If a positive quantity grows by a factor of 8, the logarithm of that ratio is 3, corresponding to three doublings. Use a ratio of like units when the interpretation is a dimensionless scale.

For a reduction by a factor of 8, the ratio is 0.125 and the result is −3. A negative logarithm is valid; it does not mean the input was negative.

The native composition =2^LOG2(3)-3 returned 0 in this run. Mathematically the inverse identity holds for every positive real x, but numerical roundtrips can leave small residuals depending on x and floating-point rounding. Do not turn this single exact-zero result into a universal equality guarantee.

The identity LOG2(a×b)=LOG2(a)+LOG2(b) applies when a and b are positive. For very large values, adding the logarithms can avoid an overflowing intermediate product. However, rounding in the logarithms still matters when nearly equal values are subtracted.

A very large positive input remains valid in the tested example: LOG2(1E300) is approximately 996.578428466209. That does not establish behavior for an input already stored as infinity or an expression that overflows before LOG2 receives it.

The empty F5 reference produced #NUM!, while TRUE became 1 and returned 0. Text “abc” failed. Check missing data and positivity before applying the formula across a column. Do not silently replace an invalid logarithm with zero, because zero is the correct logarithm of 1 and would conceal the original problem.

F5 below is an actually empty cell. The listed errors are native error results, not mathematical zeroes.

• Worksheet entry
• Numeric or argument-handling source

The retained workbook results include a deliberately stale SUM cache and an uncached SUM formula, both recalculated correctly. Native evidence covers the named 1.12.57 build and listed cases; cell-reference layouts and other explanatory compositions are instructions or independent mathematical checks unless explicitly identified as executed. Other locales, direct GUI entry and later-release output were not tested.