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Natural logs can be evaluated by adding up what is known as an 'exponential series'. The natural log of a number x, ln[x] or loge[x] is Σ[xk/k!]
    Where
  • 0<x<infinity,
  • k is every number from zero to infinity,
  • and x = eln[x] or exp[ln(x)].

Because e = e1, the base of natural logs, e, is Σ1/k! In other words, e = 1/0! + 1/1! + 1/2! + ... + 1/∞! and 2.71828 = 1/1 + 1/1 + 1/2 + 1/6 + 1/24 + 1/120 + 1/720 + 1/5040 + 1/40320