Question

(Me ajudem) - Resolva a equação exponencial : a) (1/2)^X2-4 = 8^x+2

Iguale as bases, e ache o valor de X

Answer 1

$\mathsf{\left( \dfrac{1}{2}\right)^{x^2-4}=8^{x+2} }\\\\ \mathsf{\left( \dfrac{1}{2^1}\right)^{x^2-4}=(2^3)^{x+2} }\\\\ \mathsf{(2^{-1})^{x^2-4}=2^{3x+6}}\\ \mathsf{\not2^{-x^2+4}=\not2^{3x+6}}\\\\ \mathsf{-x^2+4=3x+6}\\ \mathsf{x^2-4+3x+6=0}\\ \mathsf{x^2+3x+2=0~~(Eq.~do~2^o~grau)}\\\\ \mathsf{x_1=-1~~e~~x_2=-2}\\\\\\ \Large\boxed{\mathsf{S=\{-1,-2\}}}$