Problem 1: e^-x = x Solve for x. Problem 2: x^y - y^x = xy - x - y Solve for y.
Apr 2, 2003 #1 Ben-CS Problem 1: e^-x = x Solve for x. Problem 2: x^y - y^x = xy - x - y Solve for y. Last edited by a moderator: Apr 2, 2003
Apr 2, 2003 #2 HallsofIvy Science Advisor Homework Helper 43,008 974 Neither of these have "elementary" solutions (solutions in terms of the "elementary" functions: polynomial, rational, trig, log, exponential). The first can be solved numerically or they can be solved in terms of the "Lambert W function".
Neither of these have "elementary" solutions (solutions in terms of the "elementary" functions: polynomial, rational, trig, log, exponential). The first can be solved numerically or they can be solved in terms of the "Lambert W function".
Apr 2, 2003 #3 Graeme Problem 1: e^-x = x e^x = 1/x x e^x = 1 x = ProductLog(1), where ProductLog (a.k.a. Lambert's W-function) is defined as the inverse of f(W) = W e^W Numerically, the answer is about 0.567143290409784 Problem 2: I don't know. Sorry.
Problem 1: e^-x = x e^x = 1/x x e^x = 1 x = ProductLog(1), where ProductLog (a.k.a. Lambert's W-function) is defined as the inverse of f(W) = W e^W Numerically, the answer is about 0.567143290409784 Problem 2: I don't know. Sorry.