Log4(x-4)+log4(x-1)=1

[latex]log _{4} (x-4)+log_{4}(x-1)=1 \\ \left \{ {{x-4\ \textgreater \ 0} \atop {x-1\ \textgreater \ 0}} \right. \ \left \{ {{x\ \textgreater \ 4} \atop {x\ \textgreater \ 1}} \right. x\ \textgreater \ 4 \\ log _{4} (x-4)(x-1)=log _{4}4 \\ (x-4)(x-1)=4 \\ x^{2} -x-4x+4-4=0 \\ x^{2} -5x=0 \\ x(x-5)=0 \\ x=0, x=5[/latex] x=0 - посторонний корень. Ответ x=5