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What is a logarithm?

What is a logarithm? Here are some definitions.

Noun
  1. (mathematics) For a number
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Euler asserts that the sum of the harmonic series equals the natural logarithm of infinity plus a quantity that is nearly a constant.
The logarithm is only one of many nonlinear but monotonic functions that can be applied to measurements prior to analysis.
The logarithm remains an important mathematical function but its use in calculating has gone for ever.
The logarithm of the hazard function is linearly related to each predictor.
If the logarithm is taken as the forward function, the function taking the base to a given power is then called the antilogarithm.
It was a 17th century Scottish baron, John Napier, who first discovered the power of the logarithm as an important function in mathematics.

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