How can it be true?

Algebra Level 2

2x+2x+1+2x+2++2x+2015=4x+4x+1+4x+2++4x+2015{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 xx satisfies the equation above and it can be represented as logD(A1+BC)\log_D \left(\dfrac{A}{1+B^C} \right) for positive integers AA, BB, CC, and DD, where BB is prime, determine the smallest value of A+B+C+DA + B + C +D.

×

Problem Loading...

Note Loading...

Set Loading...