The value of $[(\log_2 9)^2]^{\frac{1}{\log_2(\log_2 9)}} \times (\sqrt{7})^{\frac{1}{\log_4 7}}$ is:
Step-by-Step Solution
Key Concept: For the first factor: let $t = \log_2(\log_2 9)$. Then $(\log_2 9)^2 = 2^{2t}$, so $[(\log_2 9)^2]^{1/t} = 2^2 = 4$. For the second: $(\sqrt{7})^{1/ \log_4 7} = 7^{1/(2 \log_4 7)} = 7^{\log_7 4/2} = 4^{1/2} = 2$. Product $= 4 \times 2 = 8$.
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Correct Answer: (1)