Why do the income and substitution effects cancel for log preferences? Trouble reconciling Slutsky decomposition I've read (pg 10) in Gourinchas' notes on consumption that the income and substitution effects cancel for log preferences, and I tried to prove this to myself doing the Slutsky decomposition for the simple case of $U(x,y) = \ln(x) + \ln(y)$ s.t. $p_x x + p_y y = I$. I get that the Hicksian and Marshallian demand functions are $x^* = \frac{p_y}{p_x} y = \frac{I}{2 p_x} $ respectively. Plugging these in gives me this for the decomposition:

$$ \frac{\partial x^*}{\partial p_x} = - \frac{p_y}{p_x^2} y - \frac{1}{2 p_x} \frac{p_y}{p_x} y $$

which is definitely not zero. Am I misunderstanding?
You interpreted the passage you read as essentially saying that "with log preferences, the Marshallian demand for the good does not depend on its price."
That doesn't sound very plausible, don't you think?

But the passage clearly refers to an intertemporal choice problem, it is about log-preferences over a single good and over time, it does not relate to the Slutsky decomposition of the static Marshallian demand function. 

I would suggest to continue reading the notes up to page 14.