Question

8) Solucione a equação exponencial abaixo.

Answer 1

$\large\boxed{\begin{array}{l}\sf 9^x+4\cdot3^x-5=0\\\sf (3^x)^2+4\cdot 3^x-5=0\\\underline{\rm fac_{\!\!,}a}\\\sf 3^x=y,com\,y>0\\\sf y^2+4y-5=0\\\sf\Delta=16+20\\\sf\Delta=36\\\sf y=\dfrac{-4\pm\sqrt{36}}{2\cdot1}\\\\\sf y=\dfrac{-4\pm6}{2}\begin{cases}\sf y_1=\dfrac{-4+6}{2}=\dfrac{2}{2}=1\\\\\sf y_2=\dfrac{-4-6}{2}=-\dfrac{10}{2}=-5\end{cases}\\\sf 3^x=1\\\sf 3^x=3^0\\\sf x=0\end{array}}$