Log3 (5 х - 6) - log72 = 3;

log0,5 (2 х + 1) = - 2;

log2 (4-2x) + log23 = 1;

log7 (x-l) = log72 + log73;

1 ≤7 х-3<49;

log2 (1 - 2 х) < 0;

lg (0,5x - 4) < 2;

log0,2 (2 х+3) ≥ - 3;

2) log0,5_ (2x+1) = - 2;

- log2_ (2x+1) = - 2;

log2_ (2x+1) = 2;

2x + 1 = 2^2;

2x = 3;

x = 1,5.

3) log2_ (4 - 2x) + log2_3 = 1;

log2_ ((4-2x) * 3 = 1;

log2_ (12 - 6x) = 1;

12 - 6x = 2^1;

12 - 6x = 2;

- 6x = - 10;

x = 10/6 = 5/3.

4) log7_ (x-1) = log7_2 + log7_3;

log7_ (x-1) = log7_ (2*3);

x - 1 = 6;

x = 7.

5) 1 ≤ 7x - 3 < 49; + 3

1 + 3 ≤ 7x < 49 + 3;

4 ≤ 7x < 52;

4/7 ≤ x < 52/7.

6) log2_ (1 - 2x) < 0;

log2_ (1 - 2x) < log2_1;

2 > 1; ⇒ 1 - 2x < 1;

- 2x < 1 - 1;

- 2x < 0; / - 2 < 0;

x > 0

7) lg (0,5 x - 4) < 2;

lg (0,5x - 4)
0,5x - 4 < 100;

0,5 x 0;

x < 208

8) log0,2_ (2x+3) ≥ - 3; 0,2 = 1/5 = 5^ (-1);

- log5_ (2x + 3) ≥ - 3; / - 1 <0;

log5_ (2x + 3) ≤ 3;

log5_ (2x+3) ≤ log5_125;

5 > 1; ⇒ 2x + 3 ≤ 125;

2 x ≤ 122;

x ≤ 61.

В первом задании не понятно условие.