Question

Solve :

${\log }_7{\log }_7\sqrt{7\sqrt{7\sqrt{7}}}$

Answer 1

We have,

${\log }_7{\log }_7\sqrt{7\sqrt{7\sqrt{7}}}$

Now,

$\Rightarrow {\log }_7{\log }_7{7}^{\frac{7}{8}}$

$\Rightarrow {\log }_7\frac{7}{8}$

$\Rightarrow {\log }_{7}7-{\log }_{7}8$

$\Rightarrow 1-{\log }_{7}8$

$\Rightarrow 1-{\log }_7{2}^3$

$\Rightarrow 1-3{\log }_{7}2$

Hence, this is the answer.