Inspired by Satyajit Mohanty

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

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 $A+B+C+D$ .

Inspiration .