Question

$\text{The value of}{\left({\left({\log }_{2}9\right)}^2\right)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times (\sqrt{7}{)}^{\frac{1}{{\log }_{4}7}}\text{is}$

Answer 1

$$\begin{array}{cc}& {\left({\left({\log }_{2}9\right)}^2\right)}^{\frac{1}{{\log }_2\left({\log }_{2}9\right)}}\times (\sqrt{7}{)}^{\frac{1}{{\log }_{4}7}}\\ & ={\left({\log }_{2}9\right)}^{{\log }_{\left({\log }_{2}9\right)}{2}^2}\times 7^{{\log }_{7}2}\\ & =2^2\times 2=8\end{array}$$