Question

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

Answer 1

Answer: 8

${\log }_2{9}^{\frac{2}{{\log }_2\left({\log }_{2}9\right)}}\times 7^{\frac{1/2}{{\log }_{4}7}}={\left({\log }_{2}9\right)}^{2{\log }_{{\log }_2{9}^2}}\times 7^{\frac{1}{2}{\log }_{7}4}$
$=4\times 2=8$