Natural logarithm function

Definition

The natural logarithm function, denoted as ln x, is the inverse of the exponential function with base e. It gives the value of y such that e raised to the power of y equals x.

Analogy

Think of the natural logarithm function as a special kind of measuring tape that helps you find the exponent needed to get a certain number. Just like a measuring tape helps you find the length of an object, ln x helps you find the exponent needed to get x.

Related terms

Exponential function: A mathematical function where a constant base is raised to a variable exponent. For example, f(x) = 2^x is an exponential function.

Logarithmic function: A mathematical function that represents the inverse relationship between exponentiation and logarithms. It allows us to solve for exponents when given a base and result.

Base e (Euler's number): A special irrational number approximately equal to 2.71828... It is commonly used in calculus and plays a significant role in exponential growth and decay functions.