Is x = 0 a valid potential solution to the equation log(x + 7) + log(x − 3) = 17?

Answer :

Plug x = 0 to check

[tex]\log(x+7) + \log(x-3)\\\\=\log(0+7) + \log(0-3)\\\\=\log 7 + \log (-3)\\\\[/tex]

You cant take log of negative number or 0 so x = 0 is not a  solution.