Rozwiąż równanie [latex] frac{1}{5-logx} + frac{2}{1+logx}=1 [/latex]

[latex]dfrac{1}{5-log x}+dfrac{2}{1+log x}=1 \ \ log x = t qquad t eq5 qquad t eq -1\ \ dfrac{1}{5-t}+dfrac{2}{1+t}=1 qquad /cdot (5-t)(1+t) \ \ 1+t+2(5-t)=(5-t)(1+t) \ \ 1+t+10-2t=5+5t-t-t^2 \ \ 11-t=-t^2+4t+5 \ \ t^2-5t+6=0 \ \ t^2-3t-2t+6=0 \ \ t(t-3)-2(t-3)=0 \ \ (t-2)(t-3)=0[/latex] [latex]t_1=2 in D \ t_2=3 in D \ \ \ log (x_1) =2 qquad lub qquad log(x_2)=3 \ \ x_1=10^2 = 100 \ x_2=10^3=1 000[/latex]