Как решать данное уравнение? (логарифмы) (log 81 по основанию x) + (log x^2 по основанию 9) - 5 = 0

logx 81 + log9 x ^ 2 - 5 = 0;

logx 9 ^ 2 + log9 x ^ 2 - 5 = 0;

2 * logx 9 + 2 * log9 x - 5 = 0;

2 * 1 / log9 x + 2 * log9 x - 5 = 0;

2 * 1 / log9 x * log9 x + 2 * log9 x * log9 x - 5 * log9 x = 0;

2 * (log9 x) ^ 2 - 5 * log9 x + 2 = 0;

Пусть log9 x = а, тогда:

2 * a ^ 2 - 5 * a + 2 = 0;

D = b ^ 2 - 4ac = (-5) ^ 2 - 4·2·2 = 25 - 16 = 9;

a1 = (5 - √9) / (2·2) = (5 - 3) / 4 = 2/4 = 0.5;

a2 = (5 + √9) / (2·2) = (5 + 3) / 4 = 8/4 = 2;

Тогда:

1) log9 x = 1 / 2;

x = 9 ^ (1/2);

x = 3;

2) log9 x = 2;

x = 9 ^ 2;

x = 81;

Ответ: х = 3 и х = 81.