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Question
If `5^(3x - 1) ÷ 25 = 125`, find the value of x.
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Solution
Given, `5^(3x - 1) ÷ 25 = 125`
∵ 25 = 5 × 5 = 52
And 125 = 5 × 5 × 5 = 53
∴ `5^(3x - 1) ÷ (5)^2 = (5)^3`
⇒ `(5)^(3x - 1 - 2) = 5^3` ...[∵ am ÷ an = (a)m – n]
⇒ `5^(3x - 3) = (5)^3`
On comparing both sides, we get
3x – 3 = 3
⇒ 3x = 6
⇒ x = 2
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