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

1.

log2(1 - x) - 2log2(1 - x) = 3;
log2(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;
2log2(x) - 3log2(x) - 5 = 0;
D = 3 + 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 = 42.