I believe your are right about the xscale options. These are regular axes to use in plots. If you want your data to show up as a straight line, change your data in stead by taking log of your x-values, when you plot. Just remember to change xlabel accordingly to show what you have done.

E.g.

plot([1,10,100],[3,2,1])
set(gca,'xscale','log')
xlabel('x')

can be shown as

plot(log10([1,10,100]),[3,2,1])
xlabel('log10(x)')

EDIT: You can alter XTick and XTickLabel manually like this in stead

set(gca,'XTick',log10(x))
set(gca,'XTickLabel',{'10^0','10^1','10^2'})

I think this can answer your question. https://youtu.be/2s3aJfRr9gE?t=284 Claude Shannon was using bits (log base 2) because he was using the uncertainty of a fair coin flip

No. There is nothing wrong with the code, it is just because floating points cannot be represented perfectly on our computers. Always use an epsilon value to allow a range of error while checking float values. Read The Floating Point Guide and this post to know more.

EDIT - As cgohlke has pointed out in the comments,

Depending on the compiler used to build numpy np.log2(x) is either computed by the C library or as 1.442695040888963407359924681001892137*np.log(x) See this link.

This may be a reason for the erroneous output.

You want

set(gca,'XTick',logfreq);

instead of set(gca,'XTickLabel',logfreq)

With your incorrect code, the 63 appears at the start and the end because there are (incorrectly) 10 x tick locations but you are specifying only 9 labels, and hence the first one is repeated. (If you'd only specified 8 then the first 2 would be repeated, etc.)