\[\large { 2 }^{ x }+{ 2 }^{ x+1 }+{ 2 }^{ x+2 }+{ 2 }^{ x+3 }={ 3 }^{ x }+{ 3 }^{ x+1 }+{ 3 }^{ x+2 }+{ 3 }^{ x+3 }\]

Given the equation above, \(x\) can be written in the form \(x=\log _{ b }{ a }.\) If \(b=\frac{2}{3},\) find the value of \(\sqrt { \frac { a }{ b } } \).

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