Question

find the value of x :- log (x+1) - log (x-1) = 1​

Answer 1

Answer:

1 & -1

Step-by-step explanation:

log a - log b = log(a/b)

log (x+1) - log (x-1) = log (x+1)/(x-1)

Given log (x+1)/(x-1) = 1(ie. log x)

Cancelling log from both sides = (x+1)/(x-1) = x

(x+1) = x(x-1)

x+1 = x^2 - x

x^2 - 2x -1 = 0

x^2 -x -x -1 = 0

x(x-1) -1(x+1) = 0

(x+1)(x-1) = 0

x = 1 & -1