Question

Find the value of ${\log }_3\left({\log }_{2}8\right)$

Answer 1

Now,

Let $a={\log }_3\left({\log }_{2}8\right)$

$={\log }_3{\log }_2{2}^3$

$={\log }_{3}3\dots (n{\log }_{a}b={\log }_a{b}^n)$

We know that, ${\log }_{a}a=1$

$a=1$.

$\therefore {\log }_3\left({\log }_{2}8\right)=1$