Решите уравнение1)[latex] \frac{1}{5-4lgx} + \frac{4}{1+lgx} =3[/latex]2)[latex]log _{3} x+log_{9}x+log_{27}x=5,5[/latex]

   [latex] \frac{1}{5-4lgx}+\frac{4}{1+lgx}=3\\ 1+lgx+20-16lgx=3(5-4lgx)(1+lgx)\\ 21-15lgx=3(5+lgx-4lg^2x)\\ 21-15lgx=15+3lgx-12lg^2x\\ 12lg^2x-18lgx+6=0\\ 2lg^2x-3lgx+1=0\\ lgx=t\\ 2t^2-3t+1=0 \\ D=1\\ t=0.5\\ t=1\\ x=10\\ x=\sqrt{10} [/latex]     [latex] log_{3}x + log_{9}x+log_{27}x=5.5\\ log_{3}x+0.5log_{3}x + \frac{log_{3}x}{3}=5.5\\ 11log_{3}x=33\\ x=27 [/latex]