Multiplication of Power Tower

Algebra Level 3

\[\large \left( 1+{ 2 }^{ { 2 }^{ 0 } } \right) \left( 1+{ 2 }^{ { 2 }^{ 1 } } \right) \left( 1+{ 2 }^{ { 2 }^{ 2 } } \right) \cdots\left( 1+{ 2 }^{ { 2 }^{ 2015 } } \right) \]

If the expression above can be expressed as \( 2^A - 1\), find the value of \(\log_2 A \).

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