The End (of the basic log tutorial)

https://arbital.com/p/log_tutorial_end

by Nate Soares Jun 17 2016 updated Sep 21 2016


That concludes our introductory tutorial on logarithms! You have made it to the end.

Throughout this tutorial, we saw that the logarithm base $~$b$~$ of $~$x$~$ calculates the number of $~$b$~$-factors in $~$x.$~$ Hopefully, this claim now means more to you than it once did. We've seen a number of different ways of interpreting what logarithms are doing, including:

For example, $~$\log_2(100)$~$ counts the number of doublings that constitute a factor-of-100 increase. (The answer is more than 6 doublings, but slightly less than 7 doublings).

We've also seen that any function $~$f$~$ whose output grows by a constant (that depends on $~$y$~$) every time its input grows by a factor of $~$y$~$ is very likely a logarithm function, and that, in essence, There is only one logarithm function.

We've glanced at the underlying structure that all logarithm functions tap into, and we've briefly discussed what makes working with logarithms so dang useful.

There are also a huge number of questions about, applications for, and extensions of the logarithm that we didn't explore. Those include, but are not limited to:

Answering these questions will require an advanced tutorial on logarithms. Such a thing does not exist yet, but you can help make it happen.