The Lambert W function is the inverse of the function f(W) = W * e^W. The Lambert W function is multi-valued, meaning that for a given value of x, there can be multiple solutions W. Lambert W function, also called Omega function or product of logarithm.

The Lambert W function has applications in various areas of mathematics, physics, and engineering, particularly in solving equations that involve exponential terms. It appears in diverse fields such as complex analysis, number theory, and differential equations.

The principal branch of the Lambert W function, denoted as W₀(x), is the real-valued branch for x in the range [0, -1/e). There are also other branches, denoted as Wₖ(x) for integer values of k, corresponding to different branches of the solution for different ranges of x. The Lambert W function is implemented in various mathematical software packages and programming languages for numerical computations.

In this video, solving the value for 'x' in the equation of x^x = 100 in terms of the Lambert 'W' Function. We utilize the natural logarithmic identities in the solution process.
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