From New Latinlogarithmus, term coined by Scottish mathematician John Napier from Ancient Greekλόγος(lógos, “word, reckoning”) and ἀριθμός(arithmós, “number”); compare rational number, from analogous Latin. The word λόγος had an original meaning of a word or a count, as in "recount a tale," or the idea of going over a list. The mathematical sense later expanded to include various specialized senses, including the notion of a ratio, proportion, or inverse proportion.
(mathematics) For a number , the power to which a given base number must be raised in order to obtain . Written . For example, because and because .
For a currency which uses denominations of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, etc., each jump in the base-10 logarithm from one denomination to the next higher is either 0.3010 or 0.3979.