Question

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

• A. $6$
• B. $10$
• C. $4$
• D. $8$

Answer 1

The correct option is D $8$

$\text{Given}:\left(\right({\log }_{2}9{)}^2{)}^{(\frac{1}{{\log }_2\left({\log }_{2}9\right)})}\times (\sqrt{7}{)}^{(\frac{1}{{\log }_{4}7})}$
$=({\log }_{2}9{)}^{\frac{2}{{\log }_2\left({\log }_{2}9\right)}}\times (7{)}^{\frac{\frac{1}{2}}{{\log }_{4}7}}$
$=({\log }_{2}9{)}^{2{\log }_{\left({\log }_{2}9\right)}2}\times (7{)}^{\frac{1}{2}{\log }_{7}4}$
$=({\log }_{2}9{)}^{{\log }_{\left({\log }_{2}9\right)}{2}^2}\times (7{)}^{{\log }_7{4}^{\frac{1}{2}}}$
$=({\log }_{2}9{)}^{{\log }_{\left({\log }_{2}9\right)}4}\times (7{)}^{{\log }_{7}2}$
$\because a^{lo{g}_{a}x}=x$
$=4\times 2$
$=8$
Hence, The correct answer is option A.