1. **State the problem:** Solve for $x$ in the equation $$x^{\frac{2}{\log x}} = x.$$ 2. **Recall the properties and formulas:** - The logarithm function $\log x$ is the logarithm base 10 unless otherwise specified. - For any positive $a$ and $b$, and any real $c$, $a^{bc} = (a^b)^c$. - If $a^m = a^n$ and $a > 0$, $a \neq 1$, then $m = n$. 3. **Rewrite the equation:** Given $$x^{\frac{2}{\log x}} = x,$$ we can write the right side as $$x^1.$$ 4. **Set the exponents equal:** Since the bases are the same and $x > 0$, $x \neq 1$, we have $$\frac{2}{\log x} = 1.$$ 5. **Solve for $\log x$:** Multiply both sides by $\log x$: $$2 = \log x.$$ 6. **Find $x$:** Recall that $\log x = 2$ means $$x = 10^2 = 100.$$ **Final answer:** $$\boxed{100}.$$