1. **State the problem:** Solve the equation $\log_2 (x + 4) - 2 \log_2 5 = 4$ for $x$. 2. **Recall logarithm properties:** - $a \log_b c = \log_b c^a$ - $\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)$ 3. **Apply the properties:** Rewrite $2 \log_2 5$ as $\log_2 5^2 = \log_2 25$. So the equation becomes: $$\log_2 (x + 4) - \log_2 25 = 4$$ 4. **Combine the logarithms:** $$\log_2 \left(\frac{x + 4}{25}\right) = 4$$ 5. **Convert logarithmic to exponential form:** $$\frac{x + 4}{25} = 2^4$$ Since $2^4 = 16$, we have: $$\frac{x + 4}{25} = 16$$ 6. **Solve for $x$:** Multiply both sides by 25: $$x + 4 = 25 \times 16 = 400$$ Subtract 4: $$x = 400 - 4 = 396$$ 7. **Check domain:** Since $x + 4 > 0$, $396 + 4 = 400 > 0$, so the solution is valid. **Final answer:** $$x = 396$$