Question

The value of ${\log }_{\sqrt{2}}\left({\log }_{\sqrt{2}}\right({\log }_{\sqrt[4]{43}}\left({\log }_{3}27\right)\left)\right)$ is

• A. $2$
• B. $3$
• C. $4$
• D. $\sqrt[3]{33}$

Answer 1

The correct option is C $4$

${\log }_{\sqrt{2}}\left({\log }_{\sqrt{2}}\right({\log }_{\sqrt[4]{43}}\left({\log }_{3}27\right)\left)\right)$
$={\log }_{\sqrt{2}}\left({\log }_{\sqrt{2}}\right({\log }_{\sqrt[4]{43}}3\left)\right)$
$={\log }_{\sqrt{2}}\left({\log }_{\sqrt{2}}4\right)$
$={\log }_{\sqrt{2}}4$
$=4$