Question

Determine o conjunto solução da seguinte equação exponencial:
$2^{x-3}+ 2^{x-1}+ 2^{x}=52$

Answer 1

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

Então:

$2^{x-3}+2^{x-1}+2^{x} = 52 \\\\ 2^{x} \cdot 2^{-3}+2^{x} \cdot 2^{-1}+2^{x} = 52 \\\\ y \cdot \frac{1}{8}+y \cdot \frac{1}{2}+y = 52 \\\\ MMC = 8 \\\\ \frac{y+4y+8y}{8} = \frac{416}{8} \\\\ 13y = 416 \\\\ \boxed{y = 32} \\\\\\ 2^{x} = y \\\\ 2^{x} = 32 \\\\ 2^{x} = 2^{5} \\\\ \boxed{\boxed{x = 5}}$