Logarithmically

Part of speech: adverb

Definitions

1. In a manner relating to the mathematical concept involving logarithms, which are exponents indicating the power to which a base must be raised to yield a given number, often used to describe scales or growth rates that change multiplicatively rather than additively
2. Characterizing processes or scales that increase or decrease according to logarithmic rules, where quantities grow in proportion to the logarithm of some variable rather than linearly or exponentially
3. Pertaining to operations or descriptions based on logarithms, such as measuring values on a logarithmic scale where equal distances correspond to equal ratios of the quantities represented rather than equal differences

Etymology: Logarithmically is a plain formation rather than a story with a famous coiner. It is built from "logarithmic," itself an adjective from "logarithm," which the Scottish mathematician John Napier introduced in 1614 in his work on tables for calculation. Napier coined "logarithm" from Greek roots meaning roughly "reckoning number" (logos, "ratio" or "reckoning," and arithmos, "number"), so the word for the mathematical idea was deliberately built from classical parts. The adjective "logarithmic" was formed by adding the Latin-derived suffix "-ic" to that noun, and the adverb "logarithmically" adds "-ally" to the adjective. The ending "-ally" descends from the Old English "-līċe," which was a common way of turning adjectives into adverbs, and it reached Middle English as "-ly" before the "-al-" link appeared in forms like "-ically." Together these pieces let English speakers describe something as changing in the manner of a logarithm.

Synonyms: exponentially, geometrically

Antonyms: linearly, arithmetically