To solve the equation [tex]\(2^{2x} = 2^3\)[/tex], we can use the property of exponents that states if the bases are the same, we can set the exponents equal to each other. Here's a step-by-step solution:
1. Given Equation:
[tex]\[
2^{2x} = 2^3
\][/tex]
2. Set the Exponents Equal:
Since the bases (2) are the same, we can set the exponents equal to each other:
[tex]\[
2x = 3
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides of the equation by 2:
[tex]\[
x = \frac{3}{2}
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].
Among the given choices:
[tex]\[
\boxed{\frac{3}{2}}
\][/tex]
