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The equation given is:

\[
1000^4 = 10^x
\]

We want to solve for \( x \).

### Step-by-step solution:

1. **Express 1000 as a power of 10:**

   \[
   1000 = 10^3
   \]

2. **Substitute this into the equation:**

   \[
   (10^3)^4 = 10^x
   \]

3. **Apply the power rule:**

   When raising a power to a power, you multiply the exponents. Thus:

   \[
   10^{12} = 10^x
   \]

4. **Equate the exponents:**

   Since the bases (10) are the same, we can set the exponents equal to each other:

   \[
   12 = x
   \]

Thus, the value of \( x \) is \( \boxed{12} \).

---

Would you like further details or clarifications on any step?

Here are some related questions to explore this topic further:

1. What is the general rule for solving equations with exponents of the same base?
2. How do you simplify expressions involving powers of powers?
3. How can you express other large numbers as powers of 10?
4. What if the base numbers were different? How would you approach the solution?
5. How would this equation change if instead of 1000, it were a number like 500?

**Tip:** When solving equations involving exponents, it's helpful to first express all terms with the same base whenever possible.

Learn how to solve the equation 1000^4 = 10^x step-by-step. Express 1000 as a power of 10, apply the power rule, and equate exponents to find x. Suitable for students in Grades 9-11.

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