Question

Combine into a single logarithm: 3log(x+y)+2log(x-y)-log(x²+y²)

i got log((x-y)²(x+y)³/x²+y²)
is this correct?

Answer 1

yeah but i think you can do some cancellation mabye

Answer 2

using the property xlogy=log(y^x), the expression becomes log((x+y)^3)+log((x-y)^2)-log(x^2 + y^2). Adding logarithmic terms are done by multiplying the variables inside, while subtracting logarithmic terms are done by dividing the variables inside. The expression when combined becomes log{[(x+y)^3][(x-y)^2]}/log(x^2+y^2)

Answer 3

oh nvm no you cannot
your answer is correct

Answer 4

thank you!!