Solve an equation with linear and exponential functions, $x=10^{x/10}$ [closed]

How to solve this equation?

$$ x = 10^{x/10} $$

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 $1.37$.

You can study and graph the two functions $y = x$ and $y = 10^{x/10}$.

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