Lg(x-1)^3-3lg(x-3)=6

lg(x-1)³-3lg(x-3)=6 ОДЗ: [latex] \left \{ {{x-1\ \textgreater \ 0} \atop {x-3\ \textgreater \ 0}} \right. , \left \{ {{x\ \textgreater \ 1} \atop {x\ \textgreater \ 3}} \right. =\ \textgreater \ [/latex] x>3. x∈(3;∞) lg(x-1)³-lg(x-3)³=6 [latex]lg \frac{(x-1) ^{3} }{(x-3) ^{3} } =6[/latex] [latex]lg( \frac{x-1}{x-3} ) ^{3} =6[/latex] [latex]( \frac{x-1}{x-3} ) ^{3} =10 ^{6} [/latex] [latex] \frac{x-1}{x-3}= 10^{2} [/latex] x-1=100*(x-3) 99x=299 x=299/99 299/99∈(3;∞) ⇒ ответ: [latex]x= \frac{299}{99} [/latex]