Неравенство плиз 5^x+1 больше 2^x+2

[latex]5^{x+1}\ \textgreater \ 2^{x+2}\\\\5^{x+1}\ \textgreater \ 2^{x+1}\cdot 2\, |:2^{x+1}\ne 0\\\\(\frac{5}{2})^{x+1}\ \textgreater \ 2\\\\(\frac{5}{2})^{x+1}\ \textgreater \ (\frac{5}{2})^{log_{\frac{5}{2}}2}\\\\x+1\ \textgreater \ log_{\frac{5}{2}}2\\\\x\ \textgreater \ log_{\frac{5}{2}}2-1\\\\x\ \textgreater \ log_{2,5}2-1[/latex]