When you enable hold on with set(groot,'defaultAxesNextPlot','add'), the figure and axes properties become locked. Thus, because the default scale is linear, your figure will remain linear even when you use the loglog (or semilogx/semilogy) command.
In this post, the Mathworks Support Team recommends to use hold on only after the loglog, semilogx or semilogy command. However, this is not possible when you preset hold on with set(groot,'defaultAxesNextPlot','add').
Therefore, you should manually change the axes scale:
x = logspace(-3,3,100);
y = (x+1)./(x+.1);
set(groot,'defaultAxesNextPlot','add')
figure
loglog(x,y)
set(gca, 'XScale', 'log','YScale', 'log') % set log-scale manually
box on % add box manually
If you don't want to add the box manually for every figure, you can also change the default setting BEFORE creating the figures with:
set(groot,'defaultAxesBox','on');
Regards
Nick
