Note that the natural log function is NOT written as ln in MATLAB, but just as log.
Next, in general, it may be impossible to plot your relationship, because there may be infinitely many disjoint regions over which your plot would need to be generated. For example, suppose you wanted to plot the regions where something as simple as sin(1./x) is between .5 and 1?
If a solution exists, where the function has a simple inverse, and if you have the symbolic toolbox, then finverse can help you.
Y = 1/(log(X) - 0.1)
Or, if you want to use plot, you could do it like this:
Y = 1/(log(X) - 0.1);
y = 5:.01:6;
xfun = matlabFunction(finverse(Y));
If you don't have the symbolic toolbox, then you would need to use a loop, and then use fzero to compute the inverse.