1. **State the problem:** Solve the equation $2^{4y} + 1 - 3 = 0$ for $y$. 2. **Simplify the equation:** Combine like terms. $$2^{4y} + 1 - 3 = 0 \implies 2^{4y} - 2 = 0$$ 3. **Isolate the exponential term:** $$2^{4y} = 2$$ 4. **Rewrite the right side as a power of 2:** $$2 = 2^1$$ 5. **Set the exponents equal:** Since the bases are the same and the function $2^x$ is one-to-one, $$4y = 1$$ 6. **Solve for $y$:** $$y = \frac{1}{4}$$ **Final answer:** $$y = \frac{1}{4}$$