Of course we all know this, so you’re preaching to the choir. However I think it would be quite demoralizing to tell a young student who is struggling with logarithms (to follow your example) that “it’s so elementary that there must be a practical use!” Indeed, middle and high school math is, to many, the most intellectually challenging thing they’ve ever had to deal with at the time these classes are taken. Considering they haven’t even taken higher order maths yet, students likely don’t have the context to realize that “elementary ≠ easy to understand”

I’ve taught at a number of “nerd camps”, generally in the fields of Gamedev and 3D modeling. I found that, more than anything else, showing young students what they can use a tool directly for triggers the imagination and inspires them to engage further with the field. These students were able to produce Google Cardboard VR content, which at the time was impressively close to the state of the art.

Anecdote: I’ve personally seen a 10-12 year old student tinker with and research the shadow settings in Unity3D [1], which is quite complicated! And she was willing and excited to put in the work because she could see with her eyes how the options affected the shadows directly. She wanted to match the shadows with a drawing she brought in.

Too bad Logarithms are not as engaging to look at as video games...

[1] https://docs.unity3d.com/Manual/ShadowOverview.html