If A = _2 _2 _4 256 + 2 _ 2 , ,2, then A is equal to - Vidyadip

Question

If $A = {\log _2}{\log _2}{\log _4}256 + 2{\log _{\sqrt 2 \,}}\,2,$ then $A$ is equal to

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Answer

c
(c) $A = {\log _2}{\log _2}{\log _4}256$ + $2{\log _2}_{^{1/2}}\,2$

$ = {\log _2}{\log _2}{\log _4}{4^4} + 2 \times {1 \over {(1/2)}}{\log _2}2$

$ = {\log _2}{\log _2}4 + 4 = {\log _2}{\log _2}{2^2} + 4$

$ = {\log _2}2 + 4 = 1 + 4 = 5$.

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