Log5 (X-8) ^2=2+2log5 (x-2) решение уравнений

Log5 (x-8) ^2=2+2log5 (x-2)

log5 (x-8) ^2=log5 (25) + log5 (x-2) ^2

log5 (x-8) ^2=log5 (25 (x-2) ^2)

(x-8) ^2=25 (x-2) ^2

x^2-16x+64=25 (x^2-4x+4)

x^2-16x+64=25x^2-100x+100

24x^2-84x+36=0 / : 12

2x^2-7x+3=0

D=49-24=25 (2 к)

x1 = (7+5) / 4=3

x2 = (7-5) / 4=0.5

Проверка:

1) log5 (3-8) ^2=log5 (25 (3-2) ^2)

log5 (25) = log5 (25)

x=3 - корень уравнения

2) log5 (0.5-8) ^2=log5 (25 (0.5-2) ^2)

log5 (56.25) = log5 (56.25)

x=0.5 - корень уравнения.

Ответ: 0.5; 3