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Question: If \(A = \log_{2}{\log_{2}{\log_{4}2}}56 + 2\log_{\sqrt{2}}{}2,\) then A is equal to...

If A=log⁡2log⁡2log⁡4256+2log⁡22,A = \log_{2}{\log_{2}{\log_{4}2}}56 + 2\log_{\sqrt{2}}{}2, then A is equal to

A

2

B

3

C

5

D

7

Answer

5

Explanation

Solution

A=log⁡2log⁡2log⁡4256A = \log_{2}{\log_{2}{\log_{4}2}}56 + 2log⁡21/222{\log_{2}{}_{1/2}}2

=log⁡2log⁡2log⁡444+2×1(1/2)log⁡22= \log_{2}{\log_{2}{\log_{4}4^{4}}} + 2 \times \frac{1}{(1/2)}\log_{2}2

=log⁡2log⁡24+4=log⁡2log⁡222+4= \log_{2}{\log_{2}4} + 4 = \log_{2}{\log_{2}2^{2}} + 4

=log⁡22+4=1+4=5= \log_{2}2 + 4 = 1 + 4 = 5.