If $5^{2x+1}÷25=125$, find the value of x.

$5^{2x+1}÷25=125$

$\Rightarrow 5^{2x+1}\times \frac{1}{25}=125$

$\Rightarrow 5^{2x+1}=125\times 25=5^3\times 5^2=5^{3+2}$

$=5^5$

$\therefore 2x+1=5\Rightarrow 2x=5-1=4$

$\Rightarrow 2x=4\Rightarrow x=\frac{4}{2}=2$

Hence x =2