Question

Determinati n e N daca 2 la puterea 2n +2 la puterea 2n+1+4 la puterea n+1=56x2 la puterea 2001

Answer 1

2^2n + 2^(2n+1) + 4^(n+1) = 
2^2n + 2^(2n+1) + (2^2)^(n+1) =
2^2n + 2^(2n+1) + 2^(2n+2) =
2^2n x (1 + 2 + 2^2) =
2^2n x 7 

2^2n x 7 = 56 x 2^2001 
2^2n x 7 = 7 x 8 x 2^2001 
2^2n x 7 = 7 x 2^3 x 2^2001 
2^2n x 7 = 7 x 2^2004 
2n = 2004 
n = 2004 : 2 
n = 1002