Question

2^x+1 + 2^x-2=9/2  <-----resolver essa equação exponencial *----* ME AJUUUUUDEM PLEAAAASE

Answer 1

2^x+1 + 2^x-2=9/2
........
2^x+1 = 2^x . 2
2^x-2 = 2^x/2² = 2^x/4, substituindo:
2^x.2 + 2^x/4 = 9/2
[4(2^x.2) + 2^x]/4 = 9/2
8.2^x + 2^x = 9.4/2
2^x(8+1) = 18
2^x = 18/9
2^x = 2 => x = 1

Answer 2

Olá Dani,

dada a equação exponencial

$2^{x+1}+2^{x-2}= \dfrac{9}{2}$

use as propriedades da exponenciação:

$2^{x}*2^{1}+2^{x}*2^{-2}= \dfrac{9}{2}\\\\ pondo~2^x~em~evid\^encia,~teremos:\\\\ 2^x*(2^1+2^{-2})= \dfrac{9}{2}\\\\ 2^x*\left( 2+\dfrac{1}{2^2}\right)= \dfrac{9}{2}\\\\ 2^x*\left(2+ \dfrac{1}{4}\right)= \dfrac{9}{2}\\\\ 2^x* \dfrac{9}{4}= \dfrac{9}{2}\\\\ 2^x= \dfrac{9}{2}: \dfrac{9}{4}\\\\ 2^x= \dfrac{9}{2}* \dfrac{4}{9}\\\\ 2^x= \dfrac{36}{18}\\\\ 2^x=2\\\\ 2^x=2^1\\\\ \not2^x=\not2^1\\\\ x=1\\\\ \boxed{S=\{1\}}$

Espero ter ajudado e tenha ótimos estudos =))