Question

The value of
$\left(\left(log_{2} \, 9\right)^{2}\right)^{\frac{1}{log_{2} \left(log_{2} \,9\right)}}\times\left(\sqrt{7}\right)^{\frac{1}{log_{4} \,7}}$
is ______

Answer 1

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