Logarithmus
Logarithmus est functio mathematica log a : R + ∖ { 0 } → R , x ↦ log a ⁡ ( x ) ,   ( a ∈ R + ∖ { 0 } ) {\displaystyle \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 ) ⇔ a y = x . {\displaystyle 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: logarithmus pro basi 10 log10(1000) lege: logarithmus decimalis quantitatis mille logarithmus naturalis seu hyperbolicus: logarithmus pro basi e (Numero Euleri). Nota: Basis in formulis saepe omittitur; itaque logarithmus decimalis scribitur lg aut log, logarithmus naturalis ln.