If A=log2log2log4(256)+2log(sqrt(2))(2),...

If `A=log_2log_2log_4(256)+2log_(sqrt(2))(2)`, then find the value of A.

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`A=log_2log_2log_4^(256)+2log_sqrt2^2`
`A=log_2log_2^4+2/sqrt2log_2^2`
`A=log_2log_2^(2^2)+4log_2^2`
`A=log_2^2+4`
`A=1+4=5`.

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