Question

помогите пожалуйста решить....

Answer 1

1. 3^(x+1) = 27^(x - 1);
 3^(x+1) = (3^3)^(x-1) ;
x+1= 3 x - 3;
 2x = 4;
 x=2.
2. 25(x+7) = 1/5;
(5^2)^(x+7) = 5^(-1);
 2x + 14 = -1;
 2x = - 15;
 x = -7,5.
3. (1/12)^(x-18) = 144^x;
 (12(-1))^(x-18) = (12^2)^x;
12^(- x +18) = 12^(2x;
 - x + 18 = -2x ;
x = -18.
4. 3*9^x = 81;
 3*9^x =3*27;
9^x = 27;
 (3^2)^x = 3^3;
2x = 3;
 x =1,5.
5. 9^(5x) - 9(5x - 1) = 8;
9 * 9^(5x-1) - 9^(5x-1) = 8;
 8* 9^(5x - 1) = 8;
9^(5x - 1) = 1;
 9^(5x - 1) = 9^0;
5x - 1 = 0;
 5x = 1;
 x=0,2.

6. 2^(x+4) + 2^(x+2) = 5^(x+1) + 3 * 5^x;
16 * 2^x + 4*2^x = 5* 5^x + 3* 5^x;
20 * 2^x = 8*5^x;
4* 5* 2^x = 4*2 * 5^x;
5*2^x = 2 *5^x;
(5/2)^x = 2/5;
(5/2)^x = (5/2)^(-1);
x = -1.
 7. 3^2x - 3^x = 72;
3^x = t >0;
 t^2 - t - 72 = 0;
 D = 1 + 4*72 = 289= 17^2;
t1 = (1+ 17) / 2= 9;
⇒ 3^x = 9 ; x = 2;
t2 = (1 - 17) / 2= - 8 < 0; ⇒решений нетю
 Ответ х = 2.
8.  (1/4)^x + (1/2)^x  -  6 = 0;
(1/2)^x = t >0;
t^2 + t - 6 = 0;
 D= 1 + 24 = 25 = 5^2;
t1 = (- 1+5) /2= 2⇒ (1/2)^x = 2;  (1/2)^x = (1/2)^(-1) ;  x = -1.;
t2 = (- 1 - 5) / 2 = - 3 <0.
Ответ х = -1.

Answer 2

а остальные?