Question

Combine into a single logarithm.
3log (x+y) + 2log(x-y) - log(x^2+y^2)

Answer 1

As a first step the coefficients of the first two terms can be eliminated giving
\[\log_{} (x+y)^{3}+\log_{} (x-y)^{2}-\log_{} (x ^{2}+y ^{2})\]
Do you understand this step?

Answer 2

I understand.

Answer 3

The next step is to use the properties of logs
\[\log a + \log b - \log c=\log\frac{a \times b}{c}\]