Question

VA IMPLOOOOOOOOOR SA-MI LUATI PCTEEEEEEEElllllle

Determinati nr. naturale care verifica relatiile:
3^x+3^x-1 =4
5*3^x-2*3^x = 81
3^2x+1-3^2x-3^2x-1-3^2x-2-3^2x-3=123
Va imploooooooooooor

Answer 1

3^x+3^x-1 =4
3^(x-1)(3^1+3^0)=4
3^(x-1)*(3+1)=4
3^(x-1)*4=4
3^(x-1)=1
3^(x-1)=3^0
x-1=0
x=1

5*3^x-2*3^x = 81
5*3^x-2*3^x = 3^4
3^x(5-2)=3^4
3^x*3=3^4
3^(x+1)=3^4
x+1=4
x=3

 3^(2x+1)-3^2x-3^(2x-1)-3^(2x-2)-3^(2x-3)=123
 3^(2x-3)(3^4-3^3-3^2-3^1-3^0)=123
 3^(2x-3)(81-27-9-3-1)=123
 3^(2x-3) *41=123
 3^(2x-3) =3^1
2x-3=1
2x=4
x=2