Răspuns :

Targoviste44id

[tex]\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[/tex]

Răspuns: [tex]\red{\underline{~\bf x = 3~}}[/tex]

Explicație pas cu pas:

[tex]\bf 3^{x}+ 3^{x-1}+3^{x-2}+3^{x-3}=40[/tex]

[tex]\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[/tex]

[tex]\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[/tex]

[tex]\bf 3^{x-3}\cdot \big(3^{3} + 3^{2}+3^{1}+3^{0}\big)=40[/tex]

[tex]\bf 3^{x-3}\cdot \big(27 + 9+3+1\big)=40[/tex]

[tex]\bf 3^{x-3}\cdot 40=40~~~~\bigg|:40[/tex]

[tex]\bf 3^{x-3} =1\implies 3^{x-3} =3^0[/tex]

[tex]\bf x-3=0\implies \red{\underline{~\bf x = 3~}}[/tex]

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