An algebra problem by Xaviery John Martinez

Algebra Level pending

Find the value of \( \log _{ 2 }{ \left[ { 2 }^{ 3 }{ 4 }^{ 4 }{ 8 }^{ 5 }{ 16 }^{ 6 }\cdots { \left( { 2 }^{ 20 } \right) }^{ 22 } \right] } . \)

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