I have a presentation in which I want to point out a difference between two functions. Instead of putting the two functions on a slide and pointing to the differences, I want to do something simple.
The first function has a form of $f_1(x) = g(x)\log (h(x))$ and the second function has the form $f_2(x) = g(x)\log(r(x)h(x))$.
The thing is that saying something along the lines "$f_2(x) - f_1(x)$ have the form of $g(x)\log r(x)$ keeps the $g(x)$ (which is rather complicated) and saying something like $f_2(x)/f_1(x)$ has the form $\log h(x) / \log (r(x)h(x))$ is also cumbersome.
Does anyone see a clear way to point out the difference between these two functions by only making explicit the additional $r(x)$?
I would really like to make it simple, ideas are welcome.