log2 (2 * x^2 + 3 * x) = log2 (6 * x + 2);

Найдем корни.

ОДЗ:

{ 2 *x^2 + 3 * x > 0;

6 * x + 2 > 0;

{ x * (2 * x + 3) > 0;

6 * x > -2;

{ x = 2;

x = -1.5;

x = -1/3;

{ x < -.5 и x > 2;

x > -1/3;

Отсюда, x > 2.

log2 (2 * x^2 + 3 * x) = log2 (6 * x + 2);

2 * x^2 + 3 * x = 6 * x + 2;

2 * x^2 - 3 * x - 2 = 0;

D = 9 - 4 * 2 * (-2) = 25;

x = (3 + 5)/4 = 2;

x = (3 - 5)/2 = -1/2;

Ответ: х = 2.