Сведем все логарифмы к основанию 3.
log9 (x-1) = log3 (√(x-1)) = 1/2*log3 (x-1)
log√3 (1/(x-1)) = -log√3 (x-1) = -log3 (x-1)^2 = -2log3 (x-1)
log(1/9) (27) = -log9 (3^3) = -3log9 (3) = -3/2
Подставляем
1/2*log3 (x-1) - 2log3 (x-1) = -3/2*log3 (x-1) = -3/2
log3 (x-1) = 1
x - 1 = 3
x = 4