Log5 (x-10)=2+log5 2 Найдите корень уравнения

[latex]log_{5} (x-10)=2+log_{5}2 [/latex] ОДЗ: [latex]x-10\ \textgreater \ 0[/latex] [latex]x\ \textgreater \ 10[/latex] [latex]log_{5} (x-10)= log_{5}5^2 +log_{5}2 [/latex] [latex]log_{5} (x-10)= log_{5}25 +log_{5}2 [/latex] [latex]log_{5} (x-10)= log_{5}(25*2)[/latex] [latex]log_{5} (x-10)= log_{5}50[/latex] [latex]x-10=50[/latex] [latex]x=60[/latex] Ответ: 60