Question

3^2x-3 + 2.3^2x= 55/3

Answer 1

E aí João,

use a propriedade da potenciação:

$3^{2x-3}+2*3^{2x}= \dfrac{55}{3}$

$3^{2x}*3^{-3}+2*3^{2x}= \dfrac{55}{3}\\\\ 3^{2x}*(3^{-3}+2)= \dfrac{55}{3}\\\\ 3^{2x}*( \dfrac{1}{27}+2)= \dfrac{55}{3}\\\\ 3^{2x}* \dfrac{55}{27}= \dfrac{55}{3}\\\\ 3^{2x}= \dfrac{55}{3}: \dfrac{55}{27}\\\\ 3^{2x}= \dfrac{55}{3}* \dfrac{27}{55}\\\\ 3^{2x}= \dfrac{1.485}{165}\\\\ 3^{2x}=9\\\\ \not3^{2x}=\not3^2\\\\ 2x=2\\\\ x= \dfrac{2}{2}\\\\ x=1\\\\\\ \boxed{S=\{1\}}$

Espero ter ajudado e tenha ótimos estudos =))