1+Log2(3x+1)=Log2(x^2-5)

   1. ОДЗ:

• 3x + 1 gt; 0;
  x - 5 gt; 0;
• x gt; -1/3;
  (x + 5)(x - 5) gt; 0;
• x (-1/3; );
  x (-; -5) (5; ).

• x (5; ).

   2. Решим:

• 1 + log2(3x + 1) = log2(x - 5);
• log2(2) + log2(3x + 1) = log2(x - 5);
• log2(2(3x + 1)) = log2(x - 5);
• 2(3x + 1) = x - 5;
• 6x + 2 - x + 5 = 0;
• 6x - x + 7 = 0;
• x - 6x - 7 = 0.

   3. Четверть дискриминанта:

• D/4 = (b/2) - ac;
• D/4 = (-3) - 1 * (-7) = 9 + 7 = 16;

• x = (-b/2 (D/4))/a;
• x = (3 16)/1 = 3 4;

• x1 = 3 - 4 = -1 (5; );
• x2 = 3 + 4 = 7 (5; ).

   Ответ: 7.