How do I create a plot that is logscale in y and mixed log/linear scale in x?

I am plotting a function on [0,180] that is nearly singular about 0. I want loglog over [0,10] and then semilogy over [10,180]. An example of the function is:

y=1/(1+2*k-cos(x)).^2;

where k is << 1.

[dpb]

Use

subplot(1,2)

to create two axes then adjust they're positions to fill in the space between, hiding the left y-axis on the RH axes. Set the two axes xlim property appropriately for the two ranges.

[dpb]

Or, the other way would be to keep the one axes object but transform x>10 to log and set the ticks and labels manually.

In this case to plot on the same axis you would

plot(log10(x>10)+10,y(x>10))

to get the offset on the axis, of course.