1. **State the problem:** We are given the function $f(x) = 1000^x$ and asked to find $x$ such that $f(x) = 10$. 2. **Write the equation:** $$1000^x = 10$$ 3. **Express both sides with the same base:** Note that $1000 = 10^3$, so we rewrite: $$ (10^3)^x = 10 $$ 4. **Simplify the left side using the power of a power rule:** $$ 10^{3x} = 10^1 $$ 5. **Since the bases are equal, set the exponents equal:** $$ 3x = 1 $$ 6. **Solve for $x$:** $$ x = \frac{1}{3} $$ 7. **Interpretation:** The value of $x$ that satisfies $1000^x = 10$ is $\frac{1}{3}$. **Final answer:** $x = \frac{1}{3}$