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.