Question

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

Answer 1

We have, $5^{2x+1}÷25=125$

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

$\Rightarrow 5^{2x+1}=125\times 25[125=5^{3}and25=5^2]$

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

$\Rightarrow 5^{2x+1}=5^5$$[\text{Using the identity},a^m\times a^n=a^{m+n}]$

$\therefore 2x+1=5$

[if base is same, then exponent will be equal on both sides of equal sign]

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

$\Rightarrow 2x=4$

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

Hence, $x=2$