Natural Logarithm

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A natural log
This page describes the monadic arithmetic function. For the dyadic logarithm function, see Logarithm.

Natural Logarithm (), or Natural Log, is a monadic scalar function which computes the natural logarithm of the argument. Logarithm shares the glyph with the dyadic arithmetic function Logarithm. The glyph, a composition of the glyphs for Circular () and Exponential (*) to indicate its close mathematical ties with these two functions, is a stylised tree log.[1]


      ⍟1 2 (*1) (*10)
0 0.6931471806 1 10


Natural logarithm is a special case of Logarithm with the default left argument of e (*1).

      ((*1)∘⍟ ≡ ⍟) 1 ¯1 0J1
Works in: Dyalog APL

Natural logarithm and exponential * are inverses of each other, except where the natural log is undefined.

      (⊢ ≡ ⍟∘*) 0 1 ¯1 0J1
      (⊢ ≡ *∘⍟) 1 ¯1 0J1 ⍝ natural log of zero is undefined
Works in: Dyalog APL

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