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Question
Solve : log5( x + 1 ) - 1 = 1 + log5( x - 1 ).
Sum
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Solution
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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