1. **State the problem:** Find the value of $$\frac{(\log_2 16)^2}{\log_2(\log_2 16)} \times \frac{\sqrt{5}}{\log_5 5}$$. 2. **Recall important formulas and rules:** - $$\log_a a = 1$$ for any base $$a$$. - $$\log_a b^c = c \log_a b$$. - Simplify step-by-step using known values. 3. **Calculate each part:** - $$\log_2 16 = 4$$ because $$2^4 = 16$$. - So, $$ (\log_2 16)^2 = 4^2 = 16$$. - Next, $$\log_2(\log_2 16) = \log_2 4 = 2$$ because $$2^2 = 4$$. - Also, $$\log_5 5 = 1$$. 4. **Substitute values into the expression:** $$\frac{16}{2} \times \frac{\sqrt{5}}{1} = 8 \times \sqrt{5}$$. 5. **Simplify the expression:** The expression simplifies to $$8 \sqrt{5}$$. 6. **Check the multiple-choice answers:** - (A) 18 - (B) 16 - (C) 8 Since $$8 \sqrt{5}$$ is approximately $$8 \times 2.236 = 17.888$$, which is closest to 18. **Final answer:** (A) 18