Solve for $x$. \[ \log _{1000} x=\frac{1}{3} \] Simplify your answer as much as possible. \[ x=\square \] $\square \log \square$ $\square \log _{\square} \square$ $\square \square$ No solution

Step 1 ：The given equation is in the form of a logarithm. To solve for x, we need to convert the logarithmic equation into an exponential equation. The base of the logarithm becomes the base of the power, the right side of the equation becomes the exponent, and x is the result.

Step 2 ：base = 1000, exponent = 0.3333333333333333, x = 9.999999999999998

Step 3 ：The calculated value of x is approximately 10. However, due to the limitations of numerical precision, the result is not exactly 10 but very close to it. We can safely assume that the result is 10.

Step 4 ：Final Answer: \(x=\boxed{10}\)