1. **State the problem:** Solve the equation $2^{3x+1} = 4$ for $x$. 2. **Recall the formula and rules:** We know that $4$ can be written as a power of $2$, since $4 = 2^2$. 3. **Rewrite the equation:** $$2^{3x+1} = 2^2$$ 4. **Since the bases are the same and nonzero, set the exponents equal:** $$3x + 1 = 2$$ 5. **Solve for $x$:** $$3x = 2 - 1$$ $$3x = 1$$ $$x = \frac{1}{3}$$ 6. **Final answer:** $$x = \frac{1}{3}$$