Question

Write the expression 3 log(x-2)+log(x+2)-log(x^2-4) as a single logarithm.

Answer 1

$3 \log(x-2)+\log(x+2)-\log(x^2-4) = 3 \log \frac{(x-2)(x+2)}{(x^2-4)}=\\=3 \log \frac{(x^2-4)}{(x^2-4)}=3\log 1= \log 1^3 = \log 1 = 0$

to answer with a single logarithm: log 1, and the value is 0