0,2^{2lg2}\quad OOF:\; x>0\\\\5\cdot (5^{-1})^{lgx}>(5^{-1})^{2lg2}\\\\5^{1-lgx}>5^{-2lg2}\\\\1-lgx>-2lg2\\\\lgx<1+2lg2\\\\lgx<lg10+lg4\\\\lgx<lg40\\\\Otvet:\; 0<x<40" alt="5\cdot 0,2^{lgx}>0,2^{2lg2}\quad OOF:\; x>0\\\\5\cdot (5^{-1})^{lgx}>(5^{-1})^{2lg2}\\\\5^{1-lgx}>5^{-2lg2}\\\\1-lgx>-2lg2\\\\lgx<1+2lg2\\\\lgx<lg10+lg4\\\\lgx<lg40\\\\Otvet:\; 0<x<40" align="absmiddle" class="latex-formula">