Question

Combine into a single logarithm. 3LOG (X+Y) + 2LOG(X-Y) - LOG(X^2 + Y^2) =

Answer 1

start with
\[\large n\log(A)=\log(A^n)\] to rewrite as
\[\large \log((x+y)^3)+\log((x-y)^2)-\log(x^2+y^2)\]

Answer 2

then
\[\log(A)+\log(B)=\log(AB)\] gives
\[\log((x+y)^3(x-y)^2)-\log(x^2+y^2)\]

Answer 3

and finally \[\log(A)-\log(B)=\log(\frac{A}{B})\]gets
\[\log(\frac{(x+y)^3(x-y)^2}{x^2+y^2}\]

Answer 4

Gracias very much !