Question

The value of ${\log }_2{\log }_2{\log }_{4}256+2{\log }_{\sqrt{2}}2$ is equal to

Answer 1

$y={\log }_2{\log }_2{\log }_{4}256+2{\log }_{\sqrt{2}}2$
$\Rightarrow y={\log }_2{\log }_2{\log }_4{4}^4+4{\log }_{2}2[\because {\log }_{a^n}{b}^m=\frac{m}{n}{\log }_{a}b\text{\&}\log a^m=m\log a\text{\&}{\log }_{a}a=1]$
$={\log }_2{\log }_2{2}^2+4$
$\Rightarrow y={\log }_{2}2+4=5$
Ans: 5