Неравенство плиз 5^x+1>2^x+2

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