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.

Defining your own using an equality such as log9(x) = log(x) / log(9) looks to be your best option.

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

k=2 log(8)/log(k)

matlab's log function (before R2017a) doesn't have this functionality. instead, you can do: log(x)/log(n), whereas log_n(x) = log(x)/log(n)

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