Question

logx (x+6)=2!pfv é atividade avaliativa​

Answer 1

Explicação passo-a-passo:

$\sf log_{x}~(x+6)=2$

$\sf x^2=x+6$

$\sf x^2-x-6=0$

$\sf \Delta=(-1)^2-4\cdot1\cdot(-6)$

$\sf \Delta=1+24$

$\sf \Delta=25$

$\sf x=\dfrac{-(-1)\pm\sqrt{25}}{2\cdot1}=\dfrac{1\pm5}{2}$

$\sf x'=\dfrac{1+5}{2}~\Rightarrow~x'=\dfrac{6}{2}~\Rightarrow~x'=3$

$\sf x"=\dfrac{1-5}{2}~\Rightarrow~x"=\dfrac{-4}{2}~\Rightarrow~x"=-2$ (não serve)

Logo, x = 3