ОДЗ:
1) x - 9 > 0
x > 9
2) lg(x - 9)² ≠ 0
lg(x - 9) ≠ 0
x - 9 ≠ 1
x ≠ 10
Пересечение: x∈(9; 10)∪(10; ∞)
( lg(x - 9) ) / 6 = 3 / ( lg(x - 9)² )
( lg(x - 9) ) / 6 = 3 / ( 2lg(x - 9) )
2lg²(x - 9) = 18 |:2
lg²(x - 9) = 9
lg²(x - 9) - 9 = 0
( lg(x - 9) - 3 )( lg(x - 9) + 3 ) = 0
1) lg(x - 9) - 3 = 0
lg(x - 9) = 3
x - 9 = 1000
x = 1009
2) lg(x - 9) + 3 = 0
lg(x - 9) = -3
x - 9 = 0,001
x = 9,001
Ответ: 9,001; 1009