Logs Meme

In the video below, Matt explores an internet meme about logarithms. Here we’ve made some questions for students to have a go at before watching the video.

This video and related activity are linked to the law: log(A × B) = log(A) + log(B). This activity is designed for sixth form students who have met this log law.

We advise students have a go at the downloadable activity before watching the video. 

In part 2) you could give your students the hint that they are looking for numbers that both sum and multiply to the same thing (i.e they are solving x + y = xy). They could generate pairs of numbers that satisfy this by fixing either x or y. We’ve also included in the downloads the spreadsheet that Matt used to do this. 

In part 3) we ask students to find more integer solutions. There is only one non-trivial integer solution; namely, x = 2 and y = 2. As part of his proof of this Matt made a plot of maximum factor sums, which we have included in the downloads. However, your students might spot that because log(1) = 0 an infinite number of trivial solutions can be made – one for every composite number. The meme is an example of one of these trivial solutions.