Question

calcule o conjunto dos seguintes sistemas de equacoes:
2×-3+2×-1+2×=52.

Answer 1

Olá,

use a propriedade da exponenciação..

$\boxed{a^{m+n}~\to~a^m\cdot a^m}\\\\ 2^{x-3}+2^{x-1}+2^x=52\\ 2^x\cdot2^{-3}+2^x\cdot2^{-1}+2^x=52\\\\ p\~oe~2^x~em~evidencia.. \\\\2^x\cdot(2^{-3}+2^{-1}+1)=52\\\\ 2^x\left( \dfrac{1}{8}+ \dfrac{1}{2}+1\right)=52\\\\ 2^x\cdot \dfrac{13}{8}=52\\\\ 2^x\cdot1,625=52\\\\ 2^x= \dfrac{52}{1,625}\\\\ 2^x=32\\ \not2^x=\not2^5\\\\ x=5\\\\\\ \huge\boxed{\boxed{S=\{5\}}}$

Tenha ótimos estudos ;D