2^x×5^x меньше 10^x^2×0.01

[latex]2^x*5^x\ \textless \ 10^{x^2}*0,01\\(2*5)^x\ \textless \ 10^{x^2}*0,01\\10^x-10^{x^2}*0,01\ \textless \ 0\\10^x(1-10^x*0,01)\ \textless \ 0\\10^x\ \textgreater \ 0\\1-10^x*0,01\ \textless \ 0\\10^x*0,01\ \textgreater \ 1\\10^x*10^{-2}\ \textgreater \ 10^0\\10^{x-2}\ \textgreater \ 10^0\\x-2\ \textgreater \ 0\\x\ \textgreater \ 2\\x\in(2;+\infty)[/latex]