Question

Resolva a função exponencial a seguir:

Answer 1

Explicação passo-a-passo:

$\sf 6^{x^2-2x-3}=1$

$\sf 6^{x^2-2x-3}=6^0$

Igualando os expoentes:

$\sf x^2-2x-3=0$

$\sf \Delta=(-2)^2-4\cdot1\cdot(-3)$

$\sf \Delta=4+12$

$\sf \Delta=16$

$\sf x=\dfrac{-(-2)\pm\sqrt{16}}{2\cdot1}=\dfrac{2\pm4}{2}$

$\sf x'=\dfrac{2+4}{2}=\dfrac{6}{2}=3$

$\sf x"=\dfrac{2-4}{2}=\dfrac{-2}{2}=-1$