Solve : Log5( X + 1 ) - 1 = 1 + Log5( X - 1 ). - Mathematics

Solve : log₅( x + 1 ) - 1 = 1 + log₅( x - 1 ).

Sum

log₅( x + 1 ) - 1 = 1 + log₅( x - 1 )

⇒ log₅( x + 1 ) - log₅( x - 1 ) = 2

⇒ `log_5 ( x + 1 )/( x - 1 ) = 2`

⇒ `( x + 1 )/( x - 1 ) = 5^2`

⇒ `( x + 1 )/( x - 1 ) = 25`
⇒ x + 1 = 25( x - 1 )
⇒ x + 1 = 25x - 25
⇒ 25x - x = 25 + 1
⇒ 24x = 26
⇒ x = `26/24 = 13/12`.

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Chapter 8: Logarithms - Exercise 8 (D) [Page 111]

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