Mathematics - Natural Logarithm

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>

<MATH> ln(1) = 0 \\ ln(e) = 1 \\ </MATH>

• Natural logarithm