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

first observer that $\log \left(x - 3\right)$ 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 $\log \left(10\right) = 1$ 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.