# 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.

$$ln(a) = \int_1^a \frac{1}{x} \, dx$$

The number e can then be defined to be the unique real number such that $$ln(e) = 1$$

## Law

$$ln(1) = 0 \\ ln(e) = 1 \\$$