Inspired by Satyajit Mohanty

Algebra Level 5

${ 3 }^{ x }+{ 3 }^{ x+1 }+\cdots+{ 3 }^{ x+31032001 }={ 27 }^{ x }+{ 27 }^{ x+1 }+\cdots+{ 27 }^{ x+31032001 }$

If the above equation is true for some integer $$x$$ and it can be expressed in the form of:-

$\large{\frac { \log _{ A }{ \left( \frac { B }{ { A }^{ C }+{ A }^{ D }+1 } \right) } }{ 2 }}$

where $$A,B,C$$ and $$D$$ are positive integers, find $$A+B+C+D$$.

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