This is somewhat a dumb question but in an article I have some function, say $f$, that depends of the variable $x$. Let's take for example the function $f$ to be given by: $$f(x)=a \log(\frac{x}{a}),$$ where $a$ is a parameter.
I now want to plot the function $f$. Since $a$ is a parameter my plot should have on the horizontal axis $x/a$ but then on the vertical axis should I label it as $\frac{1}{a} f(x)$ or $\frac{1}{a} f(\frac{x}{a})$?
I hope it's clear what I want to say. If it's confusing please let me know and i'll post some images.
Using $\frac{1}{a}f(x) = \log \left( \frac{x}{a} \right)$ is correct.
Another way of achieving what you are asking for, where $y=\left( \frac{x}{a} \right) ^{a}$, found using basic rules of manipulating logarithms.
$$ f(y) = \log(y) = \log \left( \left( \frac{x}{a} \right) ^{a} \right) $$
Personally,I would not go down this route as it complicates an otherwise simple looking function. I would use multiple line plots on the same axis with various determined values of $a$ labelled with a legend.