Question

Resolva a equação $2^{x}+ 2^{x-1} = 12$

  x = 7
  x = 4
  x = 2
  x = 12
  x = 3

Answer 1

$2^x+2^x^-^1=12\\\\ 2^x+2^x*2^-^1=12\\\\ 2^x=y\\\\ y+\frac{y}{2} =12\\\\ 2y+y = 24\\\\ 3y = 24\\\\ \boxed{y=8}$

$2^x = y\\\\ 2^x = 8\\\\ 2^x = 2^3\\\\ \boxed{x=3}$

Answer 2

Olá Gabriele,

dada a equação exponencial

$2^x+2^{x-1}=12$

use as propriedades da potenciação:

$2^x+2^x*2^{-1}=12\\\\ pondo~2^x~em~evid\^encia,~temos~que:\\\\ 2^x*(1+2^{-1})=12\\\\ 2^x*\left(1+ \dfrac{1}{2}\right)=12\\\\ 2^x* \dfrac{3}{2}=12\\\\ 2^x*3=12*2\\ 2^x*3=24\\\\ 2^x= \dfrac{24}{3}\\\\ 2^x=8\\ 2^x=2^3\\ \not2^x=\not2^3\\\\ x=3\\\\ \boxed{S=\{3\}}$

Espero ter ajudado e tenha ótimos estudos =))