Okay, let's get something straight right off the bat - logarithmic notation in maths is bad and doesn't make a whole lot of sense. And on the one hand, who cares, because maths is so much more than notation anyway. But on the other hand, it makes things way more complicated than they should be. So why don't we just find a better way?
In the video above by YouTuber 3Brown1Blue, we can see just how counterintuitive logarithmic notation actually is.
If you want to express the relationship between 2 multiplied by itself 3 times as being 8, you can use notation to express this in three completely different ways, using a position (23), a symbol (√), or a word (log).
Because, you know, maths isn't hard enough without having to learn the laws of three different languages to express the same damn thing.
"This way of writing things isn't just counterintuitive, it's countermathamatical, since rather than making seemingly different facts look the same, which is what maths should do, it takes three facts which obviously should be the same, and makes them look artificially different," says the video.
There has to be a better way. And there is.
As 3Brown1Blue explains, all you need to replace these three different ways to express the same relationship is a simple triangle. For 23 = 8, it will look like this:
All three operations that we mentioned above are now symmetrically represented on the corners of the triangle, and it looks so good:
I'll let the video take you through some more examples of this, but get ready to have maths shown to you in, well, a much more mathematical way than you've seen before.
If you've got an artistic brain and an eye for patterns - which humans are naturally pretty brilliant at seeing - then this might just change the way you think about maths. If only we could have been secretly using this on all our maths homework...
And while you're at it, why not change the way you think about addition?