Lg (x-1) + lg (x - 1) = lg8 + lg (x-2)

Решение

Lg (x-1) + lg (x - 1) = lg8 + lg (x-2)

ОДЗ: x - 1 > 0, x > 1

x - 2 > 0, x > 2

x∈ (2; + ∞)

Lg (x-1) * (x - 1) = lg8 * (x-2)

(x - 1) ² = 8x - 16

x² - 2x + 1 - 8x + 16 = 0

x² - 10x + 17 = 0

D = 100 - 4*1*17 = 32

x = (10 - 4√2) / 2

x = 5 - 2√2 не удовлетворяет ОДЗ x∈ (2; + ∞)

x = (10 + 4√2) / 2

x = 5 + 2√2

Ответ: x = 5 + 2√2