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in Logarithms by (46.2k points)

If log x – log (x – 1) = log 3, then find the value of x.

1 Answer

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Best answer

log x – log (x – 1) = log 3

⇒ log(x/(x - 1)) = log 3

On comparing,

x/(x - 1) = 3

⇒ x = 3 (x – 1)

⇒ x = 3x – 3

⇒ 3x – x = 3

⇒ 2x = 3

⇒ x = 3/2

Hence, the value of x is 3/2.

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