# Address a formula with straight and also rapid features, $x=10^{x/10}$

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There is a noticeable remedy $x = 10$. For $x > 10$ the by-product of the RHS goes to the very least $\log 10 > 1$ so there are no remedies. For $x \le 0$ there are clearly no remedies. By the IVT there is a remedy in $(0, 10)$, and also by convexity this remedy is one-of-a-kind. Actually this remedy remains in $(1, 2)$. It can be shared making use of the Lambert W - function, yet it is actually unworthy listing clearly. Numerically it has to do with $1.37$.

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Qiaochu Yuan 2019-05-08 09:15:57

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