Intuitive use of logarithms
My math teacher "taught" us about logarithms today, but he didn't give any useful information. He just that one is supposed to "add" them to create a quadratic equation. He then gave us this example;
$$ \log_4 (x + 4) + \log_4 (x - 4) $$
He then told us to solve it. This is how he did it.
$$\log_4 (x + 4) + \log_4 (x - 4)$$
$$(x + 4)(x - 4) = 0$$
$$x = -4, 4$$
This does not make a bit of sense to me. What are logarithms for? What do they do? And, most importantly, how would I actually solve this equation?