Question

Alguém poderia me ajudar! Please! 

Answer 1

$8^{x}-8^{-x}=3(1+8^{-x})$

$8^{x}-8^{-x}=3+3\cdot8^{-x}$

$8^{-x}=\dfrac{1}{8^{x}}$

$8^{x}=y$

$y-\dfrac{1}{y}=3+\dfrac{3}{y}$

$y^2-1=3y+3$

$y^2-3y-4=0$

$\Delta=(-3)^2-4\cdot1\cdot(-4)=9+16=25$

$y=\dfrac{-(-3)\pm\sqrt{25}}{2\cdot1}=\dfrac{3\pm5}{2}$

$y>0$

$y=\dfrac{3+5}{2}=\dfrac{8}{2}=4$

$8^{x}=4$

$(2^3)^{x}=2^2$

$2^{3x}=2^2$

$3x=2$

$x=\dfrac{2}{3}$