Question

soluçao da equaçao exponencial 2 elevado a x-1 -2 elevado a x+2 +56=0

Answer 1

Oi Aline,

podemos usar a propriedade da exponenciação..

$\boxed{a^{m+n}~\to~a^m\cdot a^n}\\\\\\2^{x-1}-2^{x+2}+56=0\\2^x\cdot2^{-1}-2^x\cdot2^2=-56\\\\poe~2^x~em~evidencia\\\\ 2^x\cdot(2^{-1}-2^2)=-56\\ 2^x\cdot\left( \dfrac{1}{2}-4\right)=-56\\2^x\cdot\left(- \dfrac{7}{2}\right)=-56\\\\2^x=(-56):\left( -\dfrac{7}{2}\right)\\2^x=16\\ 2^x=2^4\\ \not2^x=\not2^4\\\\ x=4\\\\\\ \huge\boxed{\boxed{S=\{4\}}}$

Tenha ótimos estudos ;D