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The natural logarithm is the logarithm function where the base has the value e
Its value is the area under the graph of the hyperbola with equation y = 1/x between x = 1 and x = a.
<MATH> ln(a) = \int_1^a \frac{1}{x} \, dx </MATH>
The number e can then be defined to be the unique real number such that <MATH> ln(e) = 1 </MATH>
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<MATH> ln(1) = 0 \\ ln(e) = 1 \\ </MATH>