Question

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

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is D $8$

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

Assuming ${\log }_{2}9=a$
$=a^{\frac{2}{{\log }_{2}a}}\times 7^{\frac{{\log }_{7}4}{2}}=a^{2{\log }_{a}2}\times 7^{{\log }_{7}2}=4\times 2=8$