Constructing solutions to Laplace equation using complex variable

If f(z) = log(z), find 2 solutions to Laplaces equation and state why Re(z)>0

Can anyone help with this?

I have that if f=u+iv, then u and v are the solutions required....

so i have u=ln(r) v=theta

or u=ln((x^2+y^2)^0.5), v=arctan(y/x)

but I cant see why Re(z)=x must be >0. I can see x=0 would be a problem but why must x>0?