I would like to generate S values from A to B both included, with a logarithmic or exponential increase between the values and I don't know which one could be a good formula to use, right now I'm using:

$\displaystyle m=B/A$

$\displaystyle f[1]=A$

$\displaystyle f[n+1]=n*(m^{1/S})$

It works well but it doesn't let me control how fast the curve grows, just the start, end and the number of steps. Is there a better one? I thought this would be a fairly used formula but I can't find a straightforward answer anywhere.