Question

Trei la puterea X + 3 la puterea X minus unu + 3 la puterea X minus doi + 3 la puterea X minus trei egal 40

Answer 1

$\it3^x+3^{x-1}+3^{x-2}+3^{x-3}=40 \Rightarrow 3^{x-3}(3^3+3^2+3+1)=40 \Rightarrow \\ \\ \Rightarrow 3^{x-3}\cdot40=40|_{:40} \Rightarrow 3^{x-3}=1 \Rightarrow 3^{x-3}=3^0\Rightarrow x-3=0 \Rightarrow x=3$

Answer 2

Răspuns: $\red{\underline{~\bf x = 3~}}$

Explicație pas cu pas:

$\bf 3^{x}+ 3^{x-1}+3^{x-2}+3^{x-3}=40$

$\bf 3^{x-3}\cdot \Big(3^{x-(x-3)} + 3^{x-1-(x-3)}+3^{x-2-(x-3)}+3^{x-3-(x-3)}\Big)=40$

$\bf 3^{x-3}\cdot \Big(3^{x-x+3} + 3^{x-1-x+3}+3^{x-2-x-+)}+3^{x-3-x+3}\Big)=40$

$\bf 3^{x-3}\cdot \big(3^{3} + 3^{2}+3^{1}+3^{0}\big)=40$

$\bf 3^{x-3}\cdot \big(27 + 9+3+1\big)=40$

$\bf 3^{x-3}\cdot 40=40~~~~\bigg|:40$

$\bf 3^{x-3} =1\implies 3^{x-3} =3^0$

$\bf x-3=0\implies \red{\underline{~\bf x = 3~}}$