# arbitrary transformation of data between linear and log-like scales

[I'm not very sure on how to formulate this question (or if it belongs here btw), so apologies in advance and I'd be happy to get feedback on other sites this question may fit better]

Suppose that I have a dataset of scores (from Min to Max). I can plot them in a linear scale. But for better resolution around (say Min) I can plot them in a log scale.

Say that I would like to implement a slider that can "cover the transformation range" between the linear and the log scales. So when the slider is "all the way left" I get a linear scale. When it is "all the way right" I have a log scale. Is there any way I can transform the scores to have values that are at any point in the transition between both "states" (linear <=> log)? The log transformation is used here as a way to describe what is the final effect I would like in the data. As far as it allows me to spread the values around Min and compress the value around Max.

Is there any continuous transformation that can allow this?