1+log2 (x+1) = log2 (7x+2) - log2 (x-1)

Вычислим корень уравнения.

1 + log2 (x + 1) = log2 (7 * x + 2) - log2 (x - 1);

Применим свойства логарифмов.

log2 2 + log2 (x + 1) = log2 (7 * x + 2) - log2 (x - 1);

log2 (2 * (x + 1)) = log2 ((7 * x + 2) / (x - 1));

2 * (x + 1) = (7 * x + 2) / (x - 1);

Умножим крест на крест.

2 * (x + 1) * (x - 1) = 7 * x + 2;

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

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

Раскроем скобки.

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

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

2 * x^2 - 7 * x - 4 = 0;

D = 49 - 4 * 2 * (-4) = 81;

x1 = (7 + 9) / 4 = 16/4 = 4;

x2 = (7 - 9) / 4 = - 2/4 = - 0.5.