Log3 (7x-11) = 4 log2 (x-7) - log2 (11-x) = 0

1) Найдем корень логарифмического уравнения:

Log3 (7 * x - 11) = 4;

7 * x - 11 = 3 ^ 4;

7 * x - 11 = 3 ^ 2 * 3 ^ 2;

7 * x - 11 = 9 * 9;

7 * x - 11 = 81;

7 * x = 81 + 11;

7 * x = 92;

x = 92/7;

2) log2 (x - 7) - log2 (11 - x) = 0;

log2 (x - 7) = log2 (11 - x);

x - 7 = 11 - x;

x + x = 11 + 7;

x + x = 18;

x * (1 + 1) = 18;

2 * x = 18;

x = 18/2;

x = 9.