1)2^2x + 14 * 2^x-1 - 29 = 0 2) LOG^6

   1) 2^(2x) + 14 * 2^(x - 1) - 29 = 0;

• 2^(2x) + 7 * 2^x - 29 = 0;
• D = 7^2 + 4 * 29 = 49 + 116 = 165;
• 2^x = (-7 165)/2;

   a) 2^x = (-7 - 165)/2 lt; 0 - нет решений;

   b) 2^x = (-7 + 165)/2;

      x = log2(165 - 7)/2.

   2) log6(x - 2) + log6(x - 1) = 1;

• x - 2 gt; 0;
  x - 1 gt; 0;
  log6((x - 2)(x - 1)) = log6(6);
• x gt; 2;
  x gt; 1;
  (x - 2)(x - 1) = 6;
• x gt; 2;
  x^2 - 3x - 4 = 0;

• D = 3^2 + 4 * 4 = 25 = 5^2;
• x = (3 5)/2;
• x1 = (3 - 5)/2 = -2/2 = -1;
• x2 = (3 + 5)/2 = 8/2 = 4;

• x gt; 2;
  x = -1; 4;

• x = 4.

   3) Переход к иному основанию:

• loga(b) = logc(b)/logc(a);

• log3(8)/log3(2) = log2(8) = 3.