If A=log2 log2 log4 256+2 log2 2, then A is equal to

A=log2 log2 log4 256+2 log21/2 2=log2 log2 log4 44+2× 11/2 log2 2=log2 log2 4+4=log2 log2 22+4=log2 2+4=1+4=5.

A=log2 log2 log4 256+2 log21/2 2=log2 log2 log4 44+2× 11/2 log2 2=log2 log2 4+4=log2 log2 22+4=log2 2+4=1+4=5.

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If $A = \log_{2} \log_{2} \log_{4} 256 + 2 \log_{\sqrt{2}} 2,$ then A is equal to

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$A = \log_{2} \log_{2} \log_{4} 256 + 2 \log_{2^{1 / 2}} 2$

$= \log_{2} \log_{2} \log_{4} 4^{4} + 2 \times \frac{1}{(1 / 2)} \log_{2} 2$

$= \log_{2} \log_{2} 4 + 4 = \log_{2} \log_{2} 2^{2} + 4$

$= \log_{2} 2 + 4 = 1 + 4 = 5 .$

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