Question

Determinati numarul natural care verifica relatiile
B. 3^x + 3^(x-1)+3^(x-2) +3^(x-3)=40

Answer 1

   
[tex]3^{x} + 3^{x-1}+3^{x-2} +3^{x-3}=40 \\ 3^{x-3+3} + 3^{x-3+2}+3^{x-3+1} +3^{x-3+0}=40 \\ 3^{x-3} \times 3^{3} + 3^{x-3} \times 3^{2}+3^{x-3} \times 3^{1} +3^{x-3} \times 3^{0}=40 \\ 3^{x-3}( 3^{3} + 3^{2}+ 3^{1} + 3^{0})=40 \\ 3^{x-3}( 27 + 9+ 3 + 1)=40 \\ 3^{x-3} \times 40=40 \\ 3^{x-3} = \frac{40}{40} \\ 3^{x-3} = 1 \\ 3^{x-3} = 3^0 \\ x-3=0 \\ x=\boxed{3}[/tex]