# How can it be true?

Algebra Level 3

${2^x + 2^{x+1} + 2^{x+2} + \ldots + 2^{x+2015} = 4^x + 4^{x+1} + 4^{x+2} + \ldots + 4^{x+2015}}$

If $$x$$ satisfies the equation above and it can be represented as

$\large{\log_D \left( \dfrac{A}{1+B^C} \right)}$

for positive integers $$A,B,C,D$$ where $$B$$ is prime, then determine the smallest value of $$A + B + C +D$$.

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