log₃(x-5)²- 4 = log√3(x-1);

ОДЗ: x ≠ 5 и x > 1.

log₃(x-5)² = log₃(x-1)² + 4;

log₃(x-5)² = log₃(x-1)² + log₃81;

log₃(x-5)² = log₃((x-1)²·81);

(x-5)² = 81(x-1)²;

x² - 10x + 25 = 81x² - 162x + 81;

81x² - 162x + 81 - x² + 10x - 25 = 0;

80x² - 152x + 56 = 0|:8;

10x² - 19x + 7 = 0

D = 361 - 280 = 81; √D = 9;

x₁ = (19 - 9)/20 = 1/2 - Не удовлетворяет ОДЗ

x₂ = (19 + 9)/20 = 28/20 = 7/5 = 1,4

Ответ: 1,4.