a: \(5^{x+1}<\left(\frac{1}{25}\right)^{\frac{1}{x}}\)
=>\(5^{x+1}<5^{-\frac{2}{x}}\)
=>\(x+1<-\frac{2}{x}\)
=>\(x+1+\frac{2}{x}<0\)
=>\(\frac{x^2+x+2}{x}<0\)
=>x<0
b: Đặt \(a=5^{x}\left(a>0\right)\)
\(5^{1+x}-5^{1-x}>24\)
=>\(5\cdot5^{x}-\frac{5}{5^{x}}>24\)
=>\(5a-\frac{5}{a}>24\)
=>\(5a^2-5>24a\)
=>\(5a^2-24a-5>0\)
=>\(5a^2-25a+a-5>0\)
=>(a-5)(5a+1)>0
=>a-5>0
=>a>5
=>\(5^{x}>5\)
=>x>1
c: \(49^{x}-6\cdot7^{x}-7<0\)
=>\(\left(7^{x}\right)^2-7\cdot7^{x}+7^{x}-7<0\)
=>\(\left(7^{x}-7\right)\left(7^{x}+1\right)<0\)
=>\(7^{x}-7<0\)
=>\(7^{x}<7\)
=>x<1
e: \(5^{2x+1}>5^{x}+4\)
=>\(25^{x}\cdot5-5^{x}-4>0\)
=>\(5\cdot\left(5^{x}\right)^2-5^{x}-4>0\)
=>\(5\cdot\left(5^{x}\right)^2-5\cdot5^{x}+4\cdot5^{x}-4>0\)
=>\(\left(5^{x}-1\right)\cdot\left(5\cdot5^{x}+4\right)>0\)
=>\(5^{x}-1>0\)
=>\(5^{x}>1=5^0\)
=>x>0
