logB(X) = logA(X) / logA(B) You can pick A to be one of the built in functions, like log or log2 or log10. E.g., log3(9) = log(9) / log(3) , or log3(9) = log10(9) / log10(3) , etc.

Probably because most other languages follow that same naming convention. Not sure why, just historical I guess.

The formula is: For any given base b, you need to compute a constant .

The log function does exactly what you want. log(14 - y) If you want a base 10 log, you use log10. There is also a log2 function, which gives a base 2 log. Other bases are achieved using the simple relation log(X)/log(b) produces a log to the base b. You could write a function for it as: logb = @(X,b) log(X)/log(b); logb(9,3) ans = 2 which is as expected. Finally, there is the reallog function, which also does the natural log, but it produces an error when the log would have been a complex number. log(-2) ans = 0.693147180559945 + 3.14159265358979i reallog(-2) Error using reallog Reallog produced complex result. But for the more normal case, reallog does the same thing as log. log(2) ans = 0.693147180559945 reallog(2) ans = 0.693147180559945

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.

Solution Given :