example: x^x = 3 I know that I can solve this equation by plotting both of the terms as a function, f(x) = x^x and g(x) = 3, and finding their intersection. But I was wondering whether there was an approach to this equation with an algebraic method or any approach that doesn't involve calculating the intersection of these functions.
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Please try to look around the site and format your question to make it easier to read. You will get more help that way! – The Count May 30 '17 at 14:27
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you can use a numerical method,e.g.the Newton Raphson method – Dr. Sonnhard Graubner May 30 '17 at 14:28
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While correct, an answer in terms of the W function doesn't make me feel any smarter. If I get an answer in terms of trig functions, I know a lot about them to give context. The W function seems essentially defining the inverse function to $x^x$ and giving it a name. – Ross Millikan May 30 '17 at 14:36
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@RossMillikan Yes, that is what the W function does. But there is a reason, namely, that this is the best we can do, since the inverse is not an elementary function. – Harald Hanche-Olsen May 30 '17 at 14:56