1. The problem is to solve the equation $\cos(3x) = 2$ for $x$. 2. Recall that the cosine function, $\cos(\theta)$, has a range of $[-1,1]$. This means $\cos(\theta)$ can never be greater than 1 or less than -1. 3. Since the right side of the equation is 2, which is outside the range of cosine, there is no real value of $x$ that satisfies $\cos(3x) = 2$. 4. Therefore, the equation has no real solutions. 5. If complex solutions are considered, one would use the inverse cosine function extended to complex numbers, but for real numbers, no solution exists.