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If log(4)(x+2y)+log(4)(x-2y)=1, then S...

If `log_(4)(x+2y)+log_(4)(x-2y)=1,` then
Statement-1: `(|x|-|y|)_(min)=sqrt(3)`
Statement-2: `AMgeGM`

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Statement-1: The solution set of the equation "log"_(x) 2 xx "log"_(2x) 2 = "log"_(4x) 2 "is" {2^(-sqrt(2)), 2^(sqrt(2))}. Statement-2 : "log"_(b)a = (1)/("log"_(a)b) " and log"_(a) xy = "log"_(a) x + "log"_(a)y