Rozwiąż równanie: [latex]log_{3} (x-2) + 0,5 log_{3} (x-4)^{2} = 0[/latex] Odpowiedź ma być: x ∈ {[latex] 3 , 3+ sqrt{2}[/latex] }

[latex]log_{3} (x-2) + 0,5 log_{3} (x-4)^{2} = 0 wedge x extgreater 2 wedge x extgreater 4\ log_{3} (x-2) + 2*0,5 log_{3} (x-4) = 0 wedge xin(4;+infty)\ log_{3} (x-2) *(x-4) = log_31\ (x-2)(x-4)=1\ x^2-6x+8=1\ x^2-6x+7=0\ Delta=36-28=8\ sqrt{Delta}=2sqrt{2}\ \ x_1=frac{6-2sqrt{2}}{2}=3-sqrt{2} ot in (4;+infty)\ x_2=3+sqrt{2}\ \ \ oxed{x=3+sqrt{2}}[/latex]