1. **State the problem:** Solve the logarithmic equation $$\log_2 4 + \log_2 (c - 9) = 5$$ for $c$. 2. **Recall the logarithm property:** The sum of logarithms with the same base can be combined as the logarithm of the product: $$\log_b A + \log_b B = \log_b (A \times B)$$ 3. **Apply the property:** $$\log_2 4 + \log_2 (c - 9) = \log_2 [4(c - 9)]$$ 4. **Rewrite the equation:** $$\log_2 [4(c - 9)] = 5$$ 5. **Convert logarithmic form to exponential form:** $$4(c - 9) = 2^5$$ 6. **Calculate the right side:** $$2^5 = 32$$ 7. **Set up the equation:** $$4(c - 9) = 32$$ 8. **Divide both sides by 4:** $$\cancel{4}(c - 9) = \frac{32}{\cancel{4}}$$ $$c - 9 = 8$$ 9. **Solve for $c$:** $$c = 8 + 9 = 17$$ 10. **Check for extraneous solutions:** The argument of the logarithm must be positive: $$c - 9 > 0 \implies 17 - 9 = 8 > 0$$ This is valid. **Final answer:** $$c = 17$$