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Algebra Level 2

2x+2x+1+2x+2+2x+3=3x+3x+1+3x+2+3x+3\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, xx can be written in the form x=logba.x=\log _{ b }{ a }. If b=23,b=\frac{2}{3}, find the value of ab\sqrt { \frac { a }{ b } } .

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