Logarithmus

Logarithmus est functio mathematica $\log _{a}:\mathbb {R} ^{+}\setminus \lbrace 0\rbrace \to \mathbb {R} ,x\mapsto \log _{a}(x),\ (a\in \mathbb {R} ^{+}\setminus \lbrace 0\rbrace )$ , cuius valor indicat exponentem variabilis independentis x ad basim a potentiae, id est: $y=\log _{a}(x)\Leftrightarrow a^{y}=x.$

Exempla:

     log₁₀(10)   = 1 quia 10¹ = 10
     log₁₀(100)  = 2 quia 10² = 100
     log₁₀(1000) = 3 quia 10³ = 1000

logarithmus decimalis seu vulgaris^[1]: logarithmus pro basi 10

log₁₀(1000) lege: logarithmus decimalis quantitatis mille

logarithmus naturalis seu hyperbolicus^[2]: logarithmus pro basi e (Numero Euleri).
Nota: Basis in formulis saepe omittitur; itaque logarithmus decimalis scribitur lg aut log, logarithmus naturalis ln.

↑ Eulerus, Leonhardus (1748). Introductio in analysin infinitorum, liber secundus, caput XXII, no. 529: "π... cujus numeri Logarithmus decimalis seu vulgaris est 0,497149872694133854351268288"
↑ Eulerus, Leonhardus (1748). Introductio in analysin infinitorum, liber primus, caput VII, no. 122: "2,71828182845904523536028... Quodsi iam ex hac basi logarithmi construantur, ii vocari solent logarithmi naturales seu hyperbolici, quoniam quadratura hyperbolae per istiusmodi logarithmos exprimi potest."

[1] Eulerus, Leonhardus (1748). Introductio in analysin infinitorum, liber secundus, caput XXII, no. 529: "π... cujus numeri Logarithmus decimalis seu vulgaris est 0,497149872694133854351268288"

[2] Eulerus, Leonhardus (1748). Introductio in analysin infinitorum, liber primus, caput VII, no. 122: "2,71828182845904523536028... Quodsi iam ex hac basi logarithmi construantur, ii vocari solent logarithmi naturales seu hyperbolici, quoniam quadratura hyperbolae per istiusmodi logarithmos exprimi potest."

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Logarithmus

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