99 Решить уравнение 1) log(2)x-2log(x)2=-1 4) log(3)x-6log(x)3=1

   1)

• log2(x) - 2logx(2) = -1;
• log2(x) - 2/log2(x) + 1 = 0;
• (log2(x))^2 + log2(x) - 2 = 0;
• D = 1^2 + 4 * 2 = 9;
• log2(x) = (-1 9)/2 = (-1 3)/2;

   a) log2(x) = (-1 - 3)/2 = -4/2 = -2;

      x = 2^(-2) = 1/4.

   b) log2(x) = (-1 + 3)/2 = 2/2 = 1;

      x = 2^1 = 2.

   4)

• log3(x) - 6logx(3) = 1;
• log3(x) - 6/log3(x) - 1 = 0;
• (log3(x))^2 - log3(x) - 6 = 0;
• D = 1^2 + 4 * 6 = 25;
• log3(x) = (1 25)/2 = (1 5)/2;

   a) log3(x) = (1 - 5)/2 = -4/2 = -2;

      x = 3^(-2) = 1/9;

   b) log3(x) = (1 + 5)/2 = 6/2 = 3;

      x = 3^3 = 27.

   Ответ:

• 1) 1/4; 2;
• 4) 1/9; 27.