The equation x^x=4 has a definitive solution: x=2. Despite initial assumptions of multiple solutions, analysis using the Newton-Raphson method confirms convergence to this single solution. Logarithmic differentiation reveals that the function has only one critical point at x=1/e, reinforcing that x=2 is the only solution. Therefore, any claims of additional solutions are incorrect.
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He's incorrect; the only solution to the equation is x=2. I can't think of an elegant proof right now, but you could use the Newton-raphson method and observe that no matter your choice for intial solution, the algorithm will always converge to 2.ssb said:I know one solution is 2 but he said there is at least one more solution.