Question

resolva a equação exponencial (1/2)^x2-4=8^x+2

Answer 1

$( \frac{1}{2} )^{x^{2}-4}=8^{x+2} \\ \\ (2^{-1})^{x^{2}-4}=8^{x+2} \\ \\(2^{-1})^{x^{2}-4}=(2^{3})^{x+2} \\ \\ -x^{2}+4=3x+6 \\ \\ x^{2}+3x+2=0 \\ \\ D = (3)^{2}-4(1)(2)=9-8=1 \\ \\ \sqrt{D} = 1 \\ \\ x' = \frac{-3+1}{2} = \frac{-2}{2} =-1 \\ \\ x'' = \frac{-3-1}{2} = \frac{-4}{2}=-2 \\ \\ x = -1 \\ou\\ x = -2$

Espero ter ajudado.