Question

знайдить корень ривняння 9^x-8*3^x-9=0

Answer 1

$9^{x} - 8 \times 3^{x} - 9 = 0 \\ \\ (3^{x}) ^{2} - 8 \times 3^{x} - 9 = 0 \\ \\ t ^{2} - 8t - 9 = 0 \\ \\ t(1) + t(2) = 8 \\ t(1) \times t(2) = - 9 \\ \\ t(1) = 9 \\ t(2) = - 1 \\ t = 3 ^{x} \\ \\ 3 ^{x} = 9 \\ x = 2 \\ \\ 3^{x} = - 1 \\ x = \times \\ \\ x = 2.$

Ответ: 2.