ln12ln3

ln12ln3 typically denotes the product of the natural logarithms of 12 and 3, i.e., ln(12) · ln(3). Since both 12 and 3 are positive, ln(12) and ln(3) are defined and positive, making the product positive as well.

In exact form, the expression can be related to other logarithms using ln(12) = ln(3) + ln(4) = ln(3) + 2 ln(2). Therefore ln(12) ln(3) = (ln(3) + 2 ln(2)) ln(3) = (ln(3))^2 + 2 ln(2) ln(3). There is no simpler closed-form expression in terms of elementary constants beyond this rewrite.

Numerically, ln(12) ≈ 2.4849066497880004 and ln(3) ≈ 1.0986122886681098, giving ln(12) ln(3) ≈ 2.72995. This value is not a well-known constant and does not simplify to a standard combination of simpler constants.

Notes and variations: Be aware that the string ln12ln3 could be misread as ln(12 ln 3) in some contexts, which is a different quantity. The latter equals ln(12 · ln(3)) and is approximately ln(13.183) ≈ 2.579. For unambiguous interpretation, the intended meaning should be stated as ln(12) · ln(3).

See also: natural logarithm, logarithm properties, product of logarithms, change of base.