Question

Помогите решить уравнение.

Answer 1

$33 \times {2}^{x - 1} - ( { {2}^{x - 1} )}^{2} = 2 \\ zamena \: {2}^{x - 1} = y \\ 33y - {y}^{2} = 2 \\ {y}^{2} - 33y + 2 = 0 \\ d = 1089 - 4 \times 1 \times 2 = 1089 - 8 = 1081. \: \: \: \sqrt{d} = + - \sqrt{1081} \\ y = \frac{33 + - \sqrt{1081} }{2} \\ {2}^{x - 1} = \frac{33 + - \sqrt{1081} }{2} \\ {2}^{x} = 33 + - \sqrt{1081} \\ x = log_{ {2} }(33 + - \sqrt{1081} )$