Question

Solve the following inequality:
$5^{2x+1}>5^x+4$

Answer 1

$5^{2x}\times 5>5^x+4$

$let{5}^x=t(t>0)$

$5t^2>t+4$

$5t^2-t-4>0$

$5t^2-5t+4t-4>0$

$5t(t-1)+4(t-1)>0$

$(t-1)(5t+4)>0$

$(t+\frac{4}{5})(t-1)>0$

$t\epsilon (-\infty ,\frac{-4}{5})\bigcup (1,\infty )$

$butt>0$

$t\epsilon (1,\infty )$

$5^x\epsilon (1,\infty )$

$x\epsilon (0,\infty )$