Question

Question 105

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

Answer 1

$5^{3x-1}÷25=125$

$\Rightarrow 5^{3x-1}÷(5{)}^2=5^3$

$\Rightarrow 5^{(3x-1)-2}=5^3$ $[a^m÷a^n=a^{m-n}]$

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

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

Since, the base is same on both sides, we can equate the exponents.

$\Rightarrow 3x-3=3\Rightarrow 3x=6\Rightarrow x=2$