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The question in the image asks which number satisfies the condition \(2^{2x} = 32\) under the given answer choices.

### Solution:
We start by solving the equation \(2^{2x} = 32\).

1. **Express 32 as a power of 2:**
   \[
   32 = 2^5
   \]
   So, the equation becomes:
   \[
   2^{2x} = 2^5
   \]

2. **Equating the exponents:**
   Since the bases are the same, we can set the exponents equal to each other:
   \[
   2x = 5
   \]

3. **Solve for \(x\):**
   \[
   x = \frac{5}{2}
   \]

Thus, the correct answer is \(x = \frac{5}{2}\).

### Answer:
The correct answer is \(\boxed{\frac{5}{2}}\).

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve for \(x\): \(2^{3x} = 128\).
2. What is the value of \(x\) if \(3^{2x} = 81\)?
3. Find the value of \(x\) for which \(5^{x+1} = 125\).
4. If \(2^{2x+1} = 64\), what is the value of \(x\)?
5. Solve for \(x\): \(4^{x-1} = 16\).

**Tip:** When solving exponential equations, it's often helpful to express both sides of the equation with the same base. This allows you to directly compare the exponents.

Which number satisfies the condition 2^{2x} = 32?

This detailed guide explains how to solve the exponential equation 2^{2x} = 32. You'll learn key algebraic concepts like expressing numbers as powers of 2 and equating exponents. Perfect for students in Grades 8-10.

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