Exponent? Variable? How?

Calculus Level 2

The function f ( x ) = x x f(x) =x^x can be written in the form e k e^k . Find the value of k k

Note : k k is not necessarily a constant.

ln x x \ln x^x Cannot be determined 2 e e

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1 solution

Max Weinstein
Apr 26, 2018

For all m m , m = e ln m m=e^{\ln {m}} plugging in m = x x m=x^x , we get that x x = e ln x x x^x=e^{\ln {x^x}} , so k = ln x x k=\ln{x^x}

Nice solution! However, please note that m cannot be 0 as ln 0 is undefined; this makes the whole expression undefined.

Raivat Shah - 3 years, 1 month ago

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Yeah, I assumed it was unnecessary to say that, because x^x cannot be 0

Max Weinstein - 3 years, 1 month ago

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Interesting insight there!

Raivat Shah - 3 years, 1 month ago

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