Question

3^(2x+1)+2.3^x=1

É urgente

Answer 1

$\large\boxed{\begin{array}{l}\sf3^{2x+1}+2\cdot3^x=1\\\sf (3^x)^2\cdot3+2\cdot 3^x=1\\\underline{\rm fac_{\!\!,}a}\\\sf 3^x=y,com\,y>0\\\sf y^2\cdot3+2\cdot y=1\\\sf 3y^2+2y-1=0\\\sf \Delta=b^2-4ac\\\sf\Delta=2^2-4\cdot3\cdot(-1)\\\sf\Delta=4+12\\\sf\Delta=16\\\sf y=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf y=\dfrac{-2\pm\sqrt{16}}{2\cdot3}\\\\\sf y=\dfrac{-2\pm4}{6}\begin{cases}\sf y_1=\dfrac{-2+4}{6}=\dfrac{2\div2}{6\div2}=\dfrac{1}{3}\\\\\sf y_2=\dfrac{-2-4}{6}=-\dfrac{6}{6}=-1\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm Quando\,y=\dfrac{1}{3}\,temos:}\\\sf 3^x=y\\\sf 3^x=\dfrac{1}{3}\\\sf x=\ell og_3\bigg(\dfrac{1}{3}\bigg)\\\\\sf S=\bigg\{ \ell og_3\bigg(\dfrac{1}{3}\bigg)\bigg\}\end{array}}$