Algebra Level 3

$\large 6+\log _{ \frac { 3 }{ 2 } }{ \left( \dfrac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\dfrac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\dfrac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\dfrac { 1 }{ 3\sqrt { 2 } } \cdots } } } \right) }$

What is the value of the expression above?

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