Răspuns: [tex]\bf n<5\implies \red{\underline{n \in \{0,1,2,3,4\}}}[/tex]
Explicație pas cu pas:
[tex]\bf \dfrac{9^n}{27^4} ~<~\dfrac{3^{10}}{81^3}[/tex]
[tex]\bf \bf \dfrac{\big(3^2\big)^n}{\big(3^2\big)^4} ~<~\dfrac{3^{10}}{\big(3^4\big)^3}[/tex]
[tex]\bf \bf \dfrac{3^{2n}}{3^{2\cdot4}} ~<~\dfrac{3^{10}}{3^{4\cdot3}}[/tex]
[tex]\bf \bf \dfrac{3^{2n}}{3^{12}} ~<~\dfrac{3^{10}}{3^{12}}[/tex]
[tex]\bf 3^{2n}:3^{12} ~<~3^{10}:3^{12}[/tex]
[tex]\bf 3^{2n-12} ~<~3^{10-12}[/tex]
[tex]\bf 3^{2n-12} ~<~3^{-2}\implies 2n-12<-2[/tex]
[tex]\bf 2n<-2+12[/tex]
[tex]\bf 2n<10~~\bigg|:2[/tex]
[tex]\bf n<5\implies \red{\underline{n \in \{0,1,2,3,4\}}}[/tex]
==pav38==
