Question

Resolva as equações exponenciais
3^2×-3^×=6

Answer 1

$3^{2x}-3^{x}=6\Rightarrow \left(3^{x}\right)^{2}-3^{x}=6$

$\ Fazemos\ \ 3^{x} =y:$

$y^{2}-y=6\Rightarrow y^{2}-y-6=0\Rightarrow y=\dfrac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}\Rightarrow\\ \\ \\ y=\dfrac{1\pm\sqrt{(-1)^{2}-4\cdot 1\cdot (-6)}}{2\cdot 1}\Rightarrow y=\dfrac{1\pm\sqrt{1+24}}{2}\Rightarrow y=\dfrac{1\pm 5}{2}\Rightarrow\\ \\ \\ y_{1}=\dfrac{1+5}{2}=3\\ \\ \\ y_{2}=\dfrac{1-5}{2}=-2$


Portanto,

$3^{x}=y\Rightarrow 3^{x}=3\Rightarrow x=1$