Question

Find the value of $x$
$5^{2x+1}÷25=125$

Answer 1

$5^{2x+1}÷25=125$

$\Rightarrow \frac{5^{2x+1}}{5^2}=5^3$

$\Rightarrow 5^{2x+1-2}=5^3$ since $\frac{a^m}{a^n}=a^{m-n}$

$\Rightarrow 5^{2x-1}=5^3$

Since bases are same, powers can be equated.

$\Rightarrow 2x-1=3$

$\Rightarrow 2x=3+1=4$ or $2x=4$ or $x=\frac{4}{2}=2$