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

1 Answer
Jul 20, 2016

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.