Log3 (x^2) = (log3 (x)) ^2

Log3 (x^2) = (log3 (x)) ^2.

2 * Log3 (x) - (log3 (x)) ^2 = 0.

(Log3 (x)) * (2 - log3 (x)) = 0.

(Log3 (x)) * (log3 3^2 - log3 (x)) = 0.

(Log3 (x)) * (log3 (9/x)) = 0.

Рассмотрим два случая.

1.) log3 (x) = 0.

log3 (x) = log3 1.

x = 1.

Сделаем проверку.

Log3 (1^2) = (log3 (1)) ^2.

Log3 1 = (log3 (1)) ^2.

0 = 0.

2.) log3 (9/x) = 0.

log3 (9/x) = log3 1.

9/x = 1.

x = 9.

Сделаем проверку.

Log3 (9^2) = (log3 (9)) ^2.

Log3 (3^4) = (log3 (3^2)) ^2.

4 = 2^2.

4 = 4.

Ответ: х = 1, х = 9.