1) log2^2 (1-x) - 2log2 (1-x) = 3 2) 2 log2x=3log3x 3) 2log2x-5logx2=3

1.

log²2 (1 - x) - 2log2 (1 - x) = 3;

log²2 (1 - x) - 2log2 (1 - x) - 3 = 0;

D/4 = 1 + 3 = 4;

log2 (1 - x) = 1 ± √4 = 1 ± 2.

1) log2 (1 - x) = 1 - 2 = - 1;

1 - x = 2^ (-1) = 1/2;

x = 1 - 1/2 = 1/2.

2) log2 (1 - x) = 1 + 2 = 3;

1 - x = 2^3 = 8;

x = 1 - 8 = - 7.

2.

2log2 (x) = 3log3 (x);

2log2 (x) = 3 * log2 (x) / log2 (3);

2log2 (3) * log2 (x) - 3log2 (x) = 0;

log2 (x) (2log2 (3) - 3) = 0;

log2 (x) = 0;

x = 1.

3.

2log2 (x) - 5logx (2) = 3;

2log2 (x) - 5/log2 (x) = 3;

2log²2 (x) - 3log2 (x) - 5 = 0;

D = 3² + 4 * 2 * 5 = 49;

log2 (x) = (3 ± √49) / 4 = (3 ± 7) / 4.

1) log2 (x) = (3 - 7) / 4 = - 1;

x = 2^ (-1) = 1/2;

2) log2 (x) = (3 + 7) / 4 = 10/4 = 5/2;

x = 2^ (5/2) = √32 = 4√2.