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

The reason that [2:2^1:256] is that the 2^1 just becomes 2, and so it's like you wrote [2:2:256].

Instead, you can think of [2^1 2^2 2^3 ...] as raising 2 to the powers [1 2 3 ...]. The operator that does that is .^, componentwise exponentiation: 2 .^ (1:8).

The only difference between linspace and logspace is that they go one step further and take the power of 10 for every element in the linspace array.

As such, you'd simply take your equation for linspace you generated, take the result and raise it to the power of 10. However, with your code, you are relying on the previous result and that is already raised to the power of 10. Therefore, you'll need to take the anti-log to convert the previous result back to a linear form, then use the same logic was used to generate the linspace, then raise it back to the power of 10. Therefore, the relationship is:

xx[n] = 10^(log10(xx[n-1]) + ((b-a)/(n-1))) 

You can certainly simplify this, taking advantage of the fact that 10^(log10(z)) = z, as long as z > 0. We can also split up the terms in the power using the property that 10^(m + n) = (10^m) * (10^n). Therefore:

xx[n] = xx[n-1] * (10^((b-a)/(n-1)))

As such, simply take your previous result multiply with 10^((b-a)/(n-1))

a = 1; b = 5; n = 7;

x = logspace(1,5,7);
xx = zeros(1,n); xx(1) = 10^a;
for i=2:n
    xx(i) = xx(i-1)*(10^((b-a)/(n-1))); %// Change 
end

We get for both x and xx:

>> format long g;
>> x

x =

  Columns 1 through 4

                        10          46.4158883361278          215.443469003188                      1000

  Columns 5 through 7

          4641.58883361278          21544.3469003189                    100000

>> xx

xx =

  Columns 1 through 4

                        10          46.4158883361278          215.443469003188                      1000

  Columns 5 through 7

          4641.58883361278          21544.3469003188                    100000

Here's a somewhat simpler way:

 logspace[a_, b_, n_] := 10.0^Range[a, b, (b - a)/(n - 1)]

This gives a sequence starting at 10^a and ending at 10^b, with n points logarithmically spaced, as does MATLAB's logspace() function.