Question

14 задание. Помогите пожалуйста решить.

Answer 1

${8}^{x} - 7 times {2}^{x + 1} + 3 times {2}^{4 - x} = 0 \ \ {8}^{x} - 7 times 2 times {2}^{x} + 3 times frac{16}{ {2}^{x} } = 0 \ \ {2}^{3x} - 14 times {2}^{x} + frac{48}{ {2}^{x} } = 0$

Пусть 2^х = t, t > 0

${t}^{3} - 14t + frac{48}{t} = 0 \ \ {t}^{4} - 14 {t}^{2} + 48 = 0$

Пусть t² = a, a > 0

a² - 14a + 48 = 0

1) a = 6

t² = 6

t = √6

2^x = √6

x = log(2)_√6

2) a = 8

t² = 8

t = √8

2^x = √8

x = log(2)_( √8 )


ОТВЕТ: log(2)_√6; log(2)_√8