How do you solve ln (x + 2) + ln (x - 2) = 0?
1 Answer
Apr 26, 2016
Take exponents of both sides to get a quadratic, the positive root of which is the solution:
x = sqrt(5)
Explanation:
Given:
ln(x+2)+ln(x-2) = 0
If we are dealing with Real logarithms then taking exponents of both sides we find:
(x+2)(x-2) = 1
That is:
x^2-4 = 1
So:
x^2 = 5
Hence:
x = +-sqrt(5)
We can discard the negative root since we require
So the remaining solution is
Footnote
If
ln t = ln abs(t) + pi i
[[ More generally
So we find:
ln(-sqrt(5)+2) + ln(-sqrt(5)-2)
= ln(sqrt(5)-2) + pi i + ln(sqrt(5)+2) + pi i = 2 pi i