Question

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

Answer 1

Given, ${\displaystyle 5^{3x-1}÷25=125}$

∵ 25 = 5 × 5 = 5²

And 125 = 5 × 5 × 5 = 5³

∴ ${\displaystyle 5^{3x-1}÷{\left(5\right)}^2={\left(5\right)}^3}$

⇒ ${\displaystyle {\left(5\right)}^{3x-1-2}=5^3}$  ...[∵ a^m ÷ aⁿ = (a)^{m – n}]

⇒ ${\displaystyle 5^{3x-3}={\left(5\right)}^3}$

On comparing both sides, we get

3x – 3 = 3

⇒ 3x = 6

⇒ x = 2