Решите уравнение: log3 (x-1) + log9 (x-1) = 3

log3 (x - 1) + log9 (x - 1) = 3;

Упростим уравнение.

log3 (x - 1) + log3^2 (x - 1) = 3;

log3 (x - 1) + 1/2 * log3 (x - 1) = 3;

Вынесем за скобки log3 (х - 1).

log3 (х - 1) * (1 + 1/2) = 3;

log3 (x - 1) * (2/2 + 1/2) = 3;

log3 (x - 1) * 3/2 = 3;

log3 (x - 1) * 1/2 = 1;

log3 (x - 1) = 2;

x - 1 = 3^2;

x - 1 = 9;

x = 9 + 1;

x = 10;

Ответ: х = 10.