1. **State the problem:** Find the value of $x$ such that $$1000^4 = 10^x.$$\n\n2. **Rewrite the base 1000 in terms of 10:** Since $1000 = 10^3$, we can write $$1000^4 = (10^3)^4.$$\n\n3. **Use the power of a power rule:** $(a^m)^n = a^{m \times n}$, so $$ (10^3)^4 = 10^{3 \times 4} = 10^{12}.$$\n\n4. **Set the expressions equal:** We have $$10^{12} = 10^x.$$\n\n5. **Since the bases are equal, the exponents must be equal:** $$x = 12.$$\n\n**Final answer:** $x = 12$