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How to solve this equation?

$ x = 10^{x/10} $

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    @Kaestur probably we should give OP the benefit of the doubt for now, then2010-08-03

2 Answers 2

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There is an obvious solution $x = 10$. For x > 10 the derivative of the RHS is at least \log 10 > 1 so there are no solutions. For $x \le 0$ there are obviously no solutions. By the IVT there is a solution in $(0, 10)$, and by convexity this solution is unique. In fact this solution is in $(1, 2)$. It can be expressed using the Lambert W-function, but it is really not worth writing down explicitly. Numerically it is about $1.37$.

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    I think the methods largely speak for themselves. If the OP has a question about them he/she should ask in a comment and I will be glad to clarify.2010-08-04
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You can study and graph the two functions $y = x$ and $y = 10^{x/10}$.

Graph of y=x and y=10^(x/10)

From which you can see that there are only two solutions.

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    Seems good now, even if I didn't reupload an$y$thing. Can you see the image now?2015-08-21