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Consider the equation xln(x)= 1 for x≥1. In this problem, you are asked to show that...

Consider the equation xln(x)= 1 for x≥1. In this problem, you are asked to show that this equation has a unique solution 1≤x <∞by completing both parts below. Note that you are not asked to find this solution, just to show that it exists and that it is unique!

(a) Show that the equation has at least one solution x such that 1≤x <∞.

(b) Show that the equation has at most one solution x such that 1≤x <∞.

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