Question

find x if ( continued in the picture)

Answer 1

${2}^{2x + 1} = 17. {2}^{x} - {2}^{3}$
$= > {2}^{2x} \times 2 = 17 \times {2}^{x} - 8$
$= > ( {2}^{x} )^{2} \times 2 = 17 \times {2}^{x } - 8$
$= > {y}^{2} \times 2 - 17 \times y + 8 = 0 \: suppose \: {2}^{x} = y$
$= > 2 {y}^{2} - 17y + 8 = 0$
$= > 2 {y}^{2} - 16y - y + 8 = 0$
$= > (2y - 1)(y - 8) = 0$
$so ....\\ y = \frac{1}{2} \\ or ...\\y = 8$
$so.... \\ {2}^{x} = {2}^{ - 1} \\ = > x = - 1 \\ or... \\ {2}^{x} = 2 ^{3} \\ = > x = 3$