Question

Rezolvati in multimea numerelor reale ecuatia log7 (x la puterea 2+8)=log7 (6x)

Answer 1

$log_{7} x^{2} - log_^{7}$6x=-8
x²-6x+8=0 => Δ=4 => x1=2 si x2=4

Answer 2

$log_{7} ( x^{2} +8)= log_{7} (6x)\\ \\C.E. \\ \\ \left \{ {{ x^{2} +8 \geq 0} \atop {6x \geq 0}} \right. \\ \\ x^{2} +8=0 \\ \\ x^{2}=-8=> x_{1,2}nu,apartin,lui R \\ [tex]D_{1}=R \\ \\ 6x=0 \\ x=0 \\ D_{2} =[0,infinit)$$\\ \\ D_{1}intersectat cuD_{2}=> D=[0,infinit)$
$log_{7} ( x^{2} +8)= log_{7} (6x) \\ \\ x^{2} +8=6x \\ \\ x^{2} -6x+8=0 \\ \\ a=1 \\ b=-6 \\ c=8$
$delta=b^{2} -4ac \\delta=36-32 \\ \\ delta=4$  $\\ \\ x_{1,2} = \frac{-b+- \sqrt{delta} }{2a} \\ \\ x_{1,2} = \frac{6+-2}{2} \\ \\ x_{1} = \frac{6-2}{2} \\ \\ x_{1}= 2 apartine domeniului\\ \\ x_{2}= \frac{6+2}{2} \\ \\ x_{2} =4apartine domeniului$