Here's an idea.
Take the scaled function: 
g(x, y; k) = log( exp(kx) + exp(ky) ) / k<p>Let k be 1/max(x,y) so that you have:<p>g(x,y) = log(exp(1)+exp(min(x,y)/max(x,y))*max(x,y)<p>There are some issues if the maximum value can be negative or zero, though.