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To solve the equation \(4^x = 64\), we need to express both sides with the same base.

### Step-by-Step Solution:

1. **Rewrite 64 as a power of 4:**

   \(64 = 4^3\) because \(4^3 = 4 \times 4 \times 4 = 64\).

2. **Set the exponents equal to each other:**

   Since the bases are the same, we can equate the exponents:
   \[
   4^x = 4^3 \implies x = 3.
   \]

3. **Conclusion:**

   The value of \(x\) is \(3\).

Would you like a detailed explanation of any part of the solution, or do you have any questions?

### Follow-up Questions:

1. How do you express numbers as powers of other numbers?
2. What is the general method for solving exponential equations?
3. What are logarithms, and how do they relate to exponential equations?
4. Can exponential equations have more than one solution?
5. How do you solve exponential equations with different bases?

**Tip:** When solving exponential equations, try to express all terms using the same base for easier comparison of exponents.

Learn how to solve the exponential equation 4^x = 64 with a detailed step-by-step solution. This problem covers key mathematical concepts including exponential equations and logarithms. Suitable for students in Grades 9-12.

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