What would be the shape of the Indifference curve with slope 1/xy?
Wolfram Alpha might come with some help. Try entering $\log x+y^2=n$ for different n's (levels of utility). You will get the idea of how the indifference curve looks like. 

e.g.
https://www.wolframalpha.com/input/?i=logx%2By%5E2+%3D+1.4