Question

How do you solve `ln (x + 2) + ln (x - 2) = 0`?

Answer 1

`x=sqrt5`

Explanation:

`ln(x+2)+ln(x-2)=0` is equivalent to

`ln[(x+2)(x-2)]=ln1`

or `(x+2)(x-2)=1`

or `x^2-4=1`

or `x^2-5=0`

or `(x+sqrt5)(x-sqrt5)=0`

or `x=-sqrt5` or `x=sqrt5`

But as `x=-sqrt5` is not in domain (as log of negative number is not possible) hence `x=sqrt5`