Question

Log3(5х – 6) - log72= 3; log0,5 (2х + 1) = -2; log2 (4-2x) + log23= 1; log7(x-l)=log72 + log73; 1 ≤7х-3<49; log2 (1 - 2х) &ltLog3(5х – 6) - log72= 3;
log0,5 (2х + 1) = -2;
log2 (4-2x) + log23= 1;
log7(x-l)=log72 + log73;
1 ≤7х-3<49;
log2 (1 - 2х) < 0;
lg (0,5x - 4) < 2;
log0,2 (2х+3) ≥ -3;

Answer 1

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) <lg100;
0,5x  - 4 < 100;
0,5 x  <  104;                  * 2>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.