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.