# Mathematics - Natural Logarithm

### Table of Contents

## About

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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## Law

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