Question

$log2log2lo{g}_{4}256+2lo{g}_{\sqrt{2}}2$

Answer 1

$\log 2\log 2{\log }_{4}256+2{\log }_{\sqrt{2}}2=\log 2\log 2{\log }_4{4}^4+2{\log }_{\sqrt{2}}{\left(\sqrt{2}\right)}^2=4\log 2\log 2+4=4(\log 2\log 2+1)=4({\left(\log 2\right)}^2+1)$