Question

$2 ^{2x +1} =17 * 2 ^{x} - 2^3$

Answer 1

2^{ 2x + 1} = 17.2^x -2³

2.(2^x)² = 17.(2^x) -8

let 2^x = P

then,

2P² = 17P -8

2P² -17P + 8 = 0

2P² -16P - P + 8 =0

2P( P - 8) -1( P -8) = 0

(2P -1)( P -8) = 0

P = 8, 1/2

so, 2^x = 8 , 1/2

2^x = 8 = 2³
x = 3

and 2^x = 1/2 = 2-¹
x = -1

hence, answer is 3 , and -1