Question

Alguém pode me ajudar a resolver essa questão? 

$0,64^{x+1} = 1,25^{-x+3}$

Obrigada!

Answer 1

$0,64^{x+1}=1,25^{-x+3}\\\\\left(\frac{64}{100}\right)^{x+1}=\left(\frac{125}{100}\right)^{-x+3}\\\\\\\left(\frac{16}{25}\right)^{x+1}=\left(\frac{5}{4}\right)^{-x+3}\\\\\\\left(\frac{4^{2}}{5^{2}}\right)^{x+1}=\left(\frac{5}{4}\right)^{-x+3}\\\\\\\left(\left[\frac{4}{5}\right]^{2}\right)^{x+1}=\left(\frac{5}{4}\right)^{-x+3}\\\\\\\left(\dfrac{4}{5}\right)^{2(x+1)}=\left(\dfrac{5}{4}\right)^{-x+3}$

Invertendo a primeira fração e trocando o sinal do expoente:

$\left(\dfrac{5}{4}\right)^{-2(x+1)}=\left(\dfrac{5}{4}\right)^{-x+3}$

Bases iguais, iguale os expoentes:

$-2(x+1)=-x+3\\-2x-2=-x+3\\-2-3=-x+2x\\-5=x\\\\\boxed{\boxed{x=-5}}$