What does antilogarithm mean?
An antilogarithm is the number that corresponds to a given logarithm — in other words, it undoes the operation of taking a logarithm. If the base-ten logarithm of a number is 2, then that number, 100, is the antilogarithm of 2; mathematically, finding an antilogarithm means raising the base to the given power. The term belongs chiefly to mathematics, engineering, and the sciences, and it carries a distinctly technical, somewhat old-fashioned flavour: before electronic calculators, students and professionals relied on printed tables of logarithms and antilogarithms to perform multiplication, division, and root extraction by hand. Today the word survives mostly in textbooks, examination syllabi, and discussions of numerical methods, where the abbreviated form 'antilog' is also common. Understanding antilogarithms remains useful for anyone working with logarithmic scales — such as pH in chemistry, decibels in acoustics, or magnitudes in astronomy — because converting a logged value back into an ordinary quantity is precisely what an antilogarithm provides.
nounThe number corresponding to a given logarithm; that is, if y is the logarithm of x, then x is the antilogarithm of y. It is the inverse operation of taking a logarithm.
- The number whose logarithm is a given value; the result of raising the base of a logarithm to the given power.
"To recover the original value from its logarithm, the engineer took the antilogarithm of 3.47."
"Since log₁₀(1000) = 3, the antilogarithm of 3 (base 10) is 1000."
"In pre-calculator chemistry labs, students used antilogarithm tables to convert pH values back into hydrogen ion concentrations."
The plural follows the standard English pattern for nouns ending in -m.
"Students once memorized pages of antilogarithms from printed reference tables."
Before pocket calculators existed, entire books of antilogarithm tables were printed so people could reverse-engineer numbers from their logs — and slide-rule users did it in their heads.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of antilogarithm
The word antilogarithm was coined in English in the 17th century as a direct compound of the prefix 'anti-' (Greek for 'against' or 'opposite') with 'logarithm', the latter itself coined around 1614 by the Scottish mathematician John Napier from Greek 'logos' ('ratio' or 'reckoning') and 'arithmos' ('number'). The name literally signals the inverse relationship: just as a logarithm converts a number into an exponent, an antilogarithm converts the exponent back into the number. It shares its Greek roots with related mathematical terms such as algorithm and arithmetic.
How antilogarithm is actually used
Antilogarithm is a technical term used mainly in mathematics, engineering, and the sciences, and appears most often in historical or educational contexts now that calculators compute exponentials directly. The shortened form 'antilog' is common in informal or classroom usage.
Easily confused with antilogarithm
A logarithm is the exponent to which a base must be raised to produce a given number, while an antilogarithm is the number produced by raising the base to that exponent — they are inverse operations.