1) 64*2^x-^1=4^x 2) 9^x-5*3^x+6=03) Iog^x-^1 (x^2-5x+7) = 1

Найдем корни уравнения.

1) 64 * 2^ (x - 1) = 4^x;

2^6 * 2^ (x - 1) = (2^2) ^x;

Применим свойства степеней.

2^ (6 * (x - 1)) = 2^ (2 * x);

6 * (x - 1) = 2 * x;

6 * x - 6 = 2 * x;

6 * x - 2 * x = 6;

4 * x = 6;

x = 6/4;

x = 3/2;

x = 1.5.

2) 9^x - 5 * 3^x + 6 = 0;

(3^x) ^2 - 5 * 3^x + 6 = 0;

Пусть 3^x = a, тогда:

a^2 - 5 * a + 6 = 0;

D = (-5) ^2 - 4 * 1 * 6 = 25 - 24 = 1;

a1 = (5 + 1) / 2 = 6/2 = 3;

a2 = (5 - 1) / 2 = 2;

Тогда:

3^x = 3;

x = 1;

3^x = 2;

x = log3 2.

3) logx^1 (x^2 - 5 * x + 7) = 1;

x^2 - 5 * x + 7 = x^1;

x^2 - 5 * x - x + 7 = 0;

x^2 - 6 * x + 7 = 0;

D = 36 - 4 * 1 * 7 = 36 - 28 = 8;

x1 = (6 + √8) / 2 = (6 + 2√2) / 2 = 3 + √2;

x2 = 3 - √2.