Question

GENTE ME SALVAA
2^x+1 + 2^x-1=9/2

Answer 1

Olá,

na equação exponencial

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

podemos desmembrar em potências de base 2, e pôr 2^x em evidência..

$2^x\cdot2^1+2^x\cdot2^{-1}= \dfrac{9}{2}\\\\ 2^x\cdot(2^1+2^{-1})= \dfrac{9}{2}\\\\ 2^x\cdot\left(2+ \dfrac{1}{2}\right)= \dfrac{9}{2}\\\\ 2^x\cdot \dfrac{5}{2}= \dfrac{9}{2}\\\\ 2^x= \dfrac{9}{2}\div \dfrac{5}{2}\\\\ 2^x= \dfrac{9}{2}\cdot \dfrac{2}{5}\\\\ 2^x= \dfrac{18}{10}\\\\ \log(2)^x=\log\left( \dfrac{18}{10}\right)\\\\ x\cdot\log(2)=\log(18)-\log(10)\\ x\cdot0,301= 1,255-1\\ x\cdot0,301=0,255\\\\ x\approx \dfrac{0,255}{0,301}\\\\ \Large\boxed{x\approx0,8472}$