Question

Solve the following inequalities
$f^{\prime }\left(x\right)>g^{\prime }\left(x\right)iff\left(x\right)=5^{2x+1}/2,g\left(x\right)=5^x+4xln5$

Answer 1

$f^{\prime }\left(x\right)>g^{\prime }\left(x\right)$

$5^{2x+1}\ln 5>5^x\log 5+4\ln 5$

$5^{2x+1}>5^x+4$

${5.5}^{2x}-5^x-4>0$

$({5.5}^x+1)(5^x-1)>0$

For every $x>0$ the inequality satisfies.