To solve the equation [tex]\( 4^{3x} = 4^2 \)[/tex], we can use the properties of exponents.
### Step-by-Step Solution:
1. Given equation:
[tex]\[
4^{3x} = 4^2
\][/tex]
2. Since the bases are the same (both are 4), we can set the exponents equal to each other:
[tex]\[
3x = 2
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{2}{3}
\][/tex]
### Conclusion:
The solution to the equation [tex]\( 4^{3x} = 4^2 \)[/tex] is [tex]\( x = \frac{2}{3} \)[/tex].
None of the other given options [tex]\(\left( x = -\frac{3}{2}, x = -\frac{2}{3}, x = \frac{3}{2} \right)\)[/tex] satisfy the equation.
Thus, the correct answer is:
[tex]\[
x = \frac{2}{3}
\][/tex]
