# 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 $$\sqrt { \frac { a }{ b } }$$.

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