Question

How do you solve `log(x+3)log(x-3)=1`?

Answer 1

There is no solution

Explanation:

first observer that `log(x-3)` means that the value of `x` must be `>3` because a log can't be negative or 0. Now in order for the product of both log terms to be `=1` both must evaluate to 1 or 1 term must be the inverse of the other. This is only possible if `x=10` because `log(10)=1` and the terms are additive inside the log and greater than 1. No matter what number `x` takes on it will be headed in both directions by 3 and they will never be equal.