Natural Logarithm Function

Natural Logarithm Function

Summary

Returns the natural logarithm of the input number. The natural logarithm function is the inverse of the exponential function.

Syntax

ln(x)

Arguments

Name Description
x the input number

Usage

Examples

Definition

The natural logarithm function describes the behavior of exponential decay which is the opposite of exponential growth. The natural logarithm function can be formally defined by the area under the hyperbola from to , or as discussed below it can also be defined as the inverse of the exponential function.

Definition of Natural Logarithm as Area Under Hyperbola from 1 to a.

Check out this video by Mathologer to see how a visual intuition can be built up using geometry.

Properties

The natural logarithm is the same as the logarithm function with a base of , Euler’s Number.