Show code, don't just tell us.
If you did
plot(f,log(x))
as it appears you must have done, then the scale is linear not log but the values are, indeed log(x) and hence, not in m (presuming that is units of x)
To show the actual dimensions on the axis that went with the data you'd have to evaluate the actual magnitude of x at each ytick value and label yticklabel with that value. Those values will then be logarithmically distributed, of course.
What would help would be to attach a figure that shows what it is you would like to achieve and a small .mat file that has some data to play with instead of having to make it up.