Select a different base for a logarithmic plot in matlab

Question

I want to have the x-axis logarithmic to the base 2: From 2^10 to 2^25 and at each step the exponent should increase by one, while the y-axis should be linear.

How is this possible? I already figured out

set(gca,'XScale','log')

but u can't set the base.

Answer 1

Consider this example:

%# some random data
x = 2.^(0:10);
y = rand(size(x));

plot(log2(x), y)                               %# plot on log2 x-scale
set(gca, 'XTickLabel',[])                      %# suppress current x-labels

xt = get(gca, 'XTick');
yl = get(gca, 'YLim');
str = cellstr( num2str(xt(:),'2^{%d}') );      %# format x-ticks as 2^{xx}
hTxt = text(xt, yl(ones(size(xt))), str, ...   %# create text at same locations
    'Interpreter','tex', ...                   %# specify tex interpreter
    'VerticalAlignment','top', ...             %# v-align to be underneath
    'HorizontalAlignment','center');           %# h-aligh to be centered

Answer 2

You can plot directly using the plot command

plot (log2(x), y)

but then your x ticks will be the logarithm rather than the actual value. You could either just change your label

xlabel('Log (base 2) of quantity X');

or you can redo the ticks manually.

xt = get(gca, 'XTick');
set (gca, 'XTickLabel', 2.^xt);

Or you can be really fancy

xticks = 10:25;
set(gca, 'XTick', xticks);
for j = 1:length(xticks)
  xtl{j} = ['2^' num2str(xticks(j))];
end
set(gca, 'XTickLabel', xtl)

which will evenly space the tick marks on the log scale, and label them according to their power of 2