Some connections between things, which I have not seen elsewhere. Maybe they mean something? 1. The Baseless Logarithm Normally one writes a logarithm with a base, \(\log_b (x)\), to mean \[y = \log_b (x) \Lra b^y = x\] And then you can change the base of the logarithm with \[\log_b (x) = \frac{\log_a (x)}{\log_a(b)}\] Which follows from rearranging \(\log_a (x) = \log_a (b^{\log_b x}) = \log_b (x) \times \log_a (b)\). One way of thinking about what this formula does is that it is a change of units, akin to writing \(2 \text{ km} = 2000 \text{ m} / \frac{1000 \text{ m}}{1 \text{ km}}\) or \(5 \text{ bytes} = 40 \text{ bits}/\frac{8 \text{ bits}}{1\text{ byte}}\). It says: how many copies of \(b\) are in \(x\)? It’s the number of copies of \(a\) in \(x\), divided by the number of copies of \(a\) that are in \(b\). This is perfectly simple, but for some reason it’s hard to think about logarithms that way. The notation kind of… obfuscates things?…