Question

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

• A. $8$
• B. $4$
• C. $6$
• D. $10$

Answer 1

The correct option is A $8$

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