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\[ 6 + \log _{ \frac { 3 }{ 2 } }{ \left( \frac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\frac { 1 }{ 3\sqrt { 2 } } \sqrt { 4-\frac { 1 }{ 3\sqrt { 2 } } \sqrt { 4 - \frac { 1 }{ 3\sqrt { 2 } } ... } } } \right) } = \ ? \]

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