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Natural logarithm

Definition

The natural logarithm function, denoted as ln(x) or loge(x), is the inverse function of exponential growth where e (approximately equal to 2.71828) is raised to the power needed to obtain x. It is commonly used in calculus and has various applications in mathematics and science.

Analogy

Think of the natural logarithm as an elevator that takes you from any floor back down to the ground floor in a building without stairs. No matter which floor you start from, this special elevator will always bring you back down smoothly.

Related terms

Exponential Function: An exponential function represents growth or decay at a constant rate over time, where the independent variable appears as an exponent.

Logarithmic Differentiation: Logarithmic differentiation is a technique that uses logarithmic properties to simplify the process of differentiating functions.

Change of Base Formula: The change of base formula allows us to express logarithms in one base as an equivalent logarithm in another base, which can be useful for calculations or comparisons.