Question

If $5^{3x-1}÷25=125$, find the value of $x$

Answer 1

Given, $5^{3x-1}÷25=125$
Since, $25=5\times 5=5^2$
And $125=5\times 5\times 5=5^3$
Therefore given equation can be written as,

$5^{3x-1}÷(5{)}^2=(5{)}^3$
$\Rightarrow (5{)}^{3x-1-2}=(5{)}^3[\because a^m÷a^n=(a{)}^{m-n}]$
$\Rightarrow (5{)}^{3x-3}=(5{)}^3$
On comparing both sides, we get
$\Rightarrow 3x-3=3$
$\Rightarrow 3x=6$
$\Rightarrow x=2$