The given equation is:

\[
2^{2x} + 3^{2x} = 4
\]

Let's solve this step by step.

### Step 1: Substitute \( y = 2^x \)
We start by substituting \( y = 2^x \). Therefore, \( 2^{2x} = (2^x)^2 = y^2 \). Now, let's handle \( 3^{2x} \).

### Step 2: Express \( 3^{2x} \) in terms of \( y \)
Now, \( 3^{2x} \) is a bit more complicated. We can leave it as it is but remember that it's independent of \( y \). The equation becomes:

\[
y^2 + 3^{2x} = 4
\]

### Step 3: Solve using possible scenarios 
We try specific values of \( x \):

#### Scenario 1: \( x = 0 \)
\[
2^{2(0)} + 3^{2(0)} = 1 + 1 = 2
\]
Does not work.

#### Scenario 2: \( x = 1 \)

Then check if \( x=2 \):

### Generalize by seeking Solution which may include logs:


Explore how to solve the exponential equation 2^(2x) + 3^(2x) = 4 step-by-step. This problem involves exponential functions and equations, requiring understanding of their properties. Suitable for Grades 10-12.

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