Решите неравенство lg x > 2-lg4
Lgx>2-lg4 lgx+lg4>2 lg(4*x)>2. 2=lg10²=lg100 lg(4x)>lg100 основание логарифма а=10. 10>1, => знак неравенства не меняем. решаем систему неравенств: x>25. x∈(25;∞)
![\left \{ {{4x\ \textgreater \ 0} \atop {4x\ \textgreater \ 100}} \right. , \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ 25}} \right. =\ \textgreater \](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B4x%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B4x%5C+%5Ctextgreater+%5C+100%7D%7D+%5Cright.+%2C++++%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7Bx%5C+%5Ctextgreater+%5C+25%7D%7D+%5Cright.+%3D%5C+%5Ctextgreater+%5C+ "\left \{ {{4x\ \textgreater \ 0} \atop {4x\ \textgreater \ 100}} \right. , \left \{ {{x\ \textgreater \ 0} \atop {x\ \textgreater \ 25}} \right. =\ \textgreater \")