Can You Solve This Olympiad Math Question? e^x = ln(x) | Lambert W Function

Can you solve this Olympiad math question? e^x = ln(x) In this video, we solve this challenging transcendental equation step by step using the Lambert W function. The equation e^x = ln(x) cannot be solved using ordinary algebraic methods, so we transform it into a form that can be solved using the Lambert W function. We obtain the exact solution: x = -W(-1) This problem is a great example of how exponential and logarithmic functions can lead to transcendental equations and how the Lambert W function can be used to find their exact solutions. In this video, you will learn: • How to transform e^x = ln(x) • How to recognize a Lambert W equation • How the Lambert W function works • How to obtain the exact solution • How to solve challenging exponential and logarithmic equations • How advanced mathematical functions can solve Olympiad-style problems If you enjoy Olympiad mathematics, challenging math problems, calculus, algebra, logarithms, exponential equations, and mathematical problem-solving, make sure to subscribe to Mathphilia for more. Like the video, share it with your friends, and comment your solution below! #Mathphilia #Mathematics #OlympiadMath #LambertW #MathProblem #MathSolution #Calculus #Algebra #Logarithms #ExponentialEquations