Question

Write log(x^2-9)-log(x+3) as a single logarithm.

Answer 1

One way: log(A)-log(B) = log(A/B) right?

So, log( x^2-9/(x+3))

Now x^2-9 = (x+3)*(x-3), and x^2-9/(x+3) = x-3,

so log(x^2-9)-log(x+3) = log(x-3),

Indeed for all x but for x = -3, but probably no one asks you about that detail?

Answer 2

b edge

Explanation: