Basic loggin'

Algebra Level 2

$\large { 2 }^{ x }+{ 2 }^{ x+1 }+{ 2 }^{ x+2 }+{ 2 }^{ x+3 }={ 3 }^{ x }+{ 3 }^{ x+1 }+{ 3 }^{ x+2 }+{ 3 }^{ x+3 }$

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