Question

lg^2 (x-1)-2lg(x-1)+1=0

Answer 1

ОДЗ: x>1

$log {}^{2} (x - 1) - 2 log(x - 1) + 1 = 0 \\ log(x - 1) = a \\ a {}^{2} - 2a + 1 = 0 \\ (a - 1) {}^{2} = 0 \\ a - 1 = 0 \\ a = 1$

сделаем обратную замену

$a = log(x - 1) \\ log(x - 1) = 1$

$x - 1 = 10 {}^{1} \\ x - 1 = 10 \\ x = 10 + 1 \\ x = 11$

$x = 11 \\ x > 1$

$x = 11 \\ otvet$