# How can it be true?

Algebra Level 2

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

If $x$ satisfies the equation above and it can be represented as $\log_D \left(\dfrac{A}{1+B^C} \right)$ for positive integers $A$, $B$, $C$, and $D$, where $B$ is prime, determine the smallest value of $A + B + C +D$.

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