Question

solve the equation:
⇒ log(x+1) - log(x-1) = 1

Answer 1

Hey there !

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

We know that,

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

Applying this formula we get,

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

=> ( x + 1 / x - 1 ) = n¹ ( n = base )

=> x + 1 = n ( x - 1 )

=> x + 1 = nx - n

=> x - nx = -1 -n

=> x ( 1 - n ) = - 1 - n

=> x = - 1 - n / 1 - n

=> x = - 1 ( 1 + n ) / 1 - n

=> x = 1 + n / n - 1

According to the question, base in the log function is 10.

So substituting n = 10 we get,

=> x = 1 + 10 / 10 - 1

=> x = 11 / 9

Hope my answer helped !