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Natalie, If f(x) = ln(x)/x and the maximum value of f(x) occurs at x = e the f(e) > f(π). Thus
But ln(e) = 1 so
Can you manipulate this inequality to show that e^{π} > π^{e}? If so then all that remains is to show that the maximum value of f(x) occurs at x = e. I used calculus. Harley  


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