'inverse-logarithmic' is a compound of 'inverse' and 'logarithmic'. 'Inverse' originates from Latin, specifically the past participle 'inversus' from 'invertere', where 'in-' meant 'not/toward' and 'vertere' meant 'to turn'. 'Logarithmic' originates from New Latin/Modern English formation based on Greek 'logarithmos' (see below).

'inverse' entered English via Old French/Latin influences as 'inverse'/'inversus' and became the modern English adjective 'inverse'. 'Logarithmic' was formed in English from 'logarithm' (coined in the early 17th century) plus the adjectival suffix '-ic', producing 'logarithmic'; the compound 'inverse-logarithmic' is a modern English technical coinage combining the two.

Initially, 'inverse' simply conveyed 'turned inside out or reversed' (from Latin), and 'logarithmic' referred to properties of logarithms. Combined in modern technical usage, 'inverse-logarithmic' specifically denotes the reversal or inverse operation/scale of a logarithmic function or effect.