2003 AMC 12B Problem 17

Let $X = \log x$ and $Y = \log y.$ Then $$X + 3Y = 1$$ and $$2X + Y = 1.$$ Solving gives $X = \dfrac{2}{5}$ and $Y = \dfrac{1}{5},$ so $$\log(xy) = X + Y = \frac{3}{5}.$$ Thus, the correct answer is D.