Question

7 la puterea x+3 - 7 la puterea x+2 - 7 la puterea x+1=41*7 la puterea 2x;
Calculati x

Answer 1

7^(x+3)- 7^(x+2) - 7^(x+1) = 41 * 7^(2x)

7^x * (7^3 - 7^2 - 7) = 41 * 7^(2x)

7^x * (343 - 49 - 7) = 41 * 7^2x

7^x * 287 = 41 * 7^2x

7^x * 7 * 41 = 41 * 7^2x

7^2x * 41 = 41 * 7^2x

x poate fi orice numar natural