This is indeed a fit of a power law, which can be described with the formula y = k * x^tau. If you plot this in a log-log figure, you get a straight line. To retrieve the parameters, you have to take the logarithm of both sides of the equation, and then do a linear fit:

% generate some data with random noise
x = logspace(-.5, 1.5, 100);
y = 42 * x.^0.66;
y = y .* (1 + 0.2 * randn(size(y)));

% do linear fit: log(y) = p(1) * log(x) + p(2)
p = polyfit(log(x), log(y), 1);

% retrieve original parameters
tau = p(1);
k = exp(p(2));

% plot
loglog(x, y, '.', x, k*x.^tau, 'r')
axis([.1 100 10 1000])
legend('data', sprintf('power law fit: y = %.1f * x^{%.2f}', k, tau))
xlabel('Amplitude')
ylabel('Velocity')

Result: Note that this is just a quick and dirty trick, it probably does not give a result that is statistically correct.

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