Решите уравнения 1)(x-1)^3=27 2)(5x)^2=100 3)2^2n=256 4)6^(2k-1)=216

Вычислим корешки.

1) (x - 1)^3 = 27; 

(x - 1)^3 = 3^3; 

x - 1 = 3;

x = 3 + 1;

x = 4;

Ответ: х = 4.

2) (5 * x)^2 = 100; 

(5 * x)^2 - 10^2 = 0; 

(5 * x - 10) * (5 * x + 10) = 0;

5  * x - 10 = 0;

5 * x + 10 = 0;

5 * x = 10;

5 * x = -10;

x = 10/5;

x = -10/5;

x = 2;

x = -2.

3) 2^(2 * n) = 256; 

2^(2 * n) = 2^8; 

2 * n = 8; 

n = 8/2; 

n = 4. 

4) 6^(2 * k - 1) = 216;  

6^(2 * k - 1) = 6^3; 

2 * k - 1 = 3; 

2 * k = 3 + 1; 

2 * k = 4; 

k = 4/2; 

k = 2.