Question

Poderiam resolver esta conta?
$3^{x+1} -3^{x-1}=216$

Answer 1

Olá Bruno,

use a propriedade da exponenciação:

$a^{m+n}~\to~a^m*a^n\\\\ a^{-1}~\to~ \dfrac{1}{a^1}~\to~ \dfrac{1}{a}$

______________________

$3^{x+1}-3^{x-1}=216\\ 3^x*3^1-3^x*3^{-1}=216~\to~3^x~em~evidencia:\\\\ 3^x*(3^1-3^{-1})=216\\\\ 3^x*\left(3- \dfrac{1}{3}\right)=216\\\\ 3^x* \dfrac{8}{3}=216\\\\ 8*3^x=216*3\\ 8*3^x=648\\\\ 3^x= \dfrac{648}{8}\\\\ 3^x=81\\\\ \not3^x=\not3^4\\\\ x=4\\\\ \boxed{S=\{4\}}$

Bons estudos =))