I studied Mathematics and Further Mathematics at college and logarithms always stumped me. I understood log base 10 by past that, I just couldn’t get my head around it. If only I had Toby Hendy to help me.

Toby is what’s known as an “EduTuber” (educational YouTuber) and she runs her channel, Tibees, to teach people about the joys of physics and mathematics. The channel is so popular, she withdrew from her PhD and gone full-time with it. In an interview with Westpac, she explained why:

“I’d always thought after I finished my PhD I’d become a lecturer at a university and be able to teach students in that way, but when I started teaching online and was already getting huge numbers, I realised it doesn’t even compare […] You could have a video that you’ve made in your bedroom getting a million views but you could never reach that many in a classroom. The way it scales is extremely powerful.”

## The art of logarithms

Amongst her hundreds of videos is this one about logarithms. But rather than give a turgid lecture on inverse functions and exponentiation, Toby delivered her lesson in the style of iconic painter Bob Ross. In fact, the video comes as part of a whole series called *The Joy of Mathematics* in honour of him. The video starts with her drawing trees on a blackboard overlooking some woods in an attempt to relax the viewer. Then she uses the trees to explaining exponential growth (you know that thing people keep talking about in relation to how COVID-19 is spreading?)

## The base terms of logarithms

- Exponentiation – a mathematical operation involving raising a base to an exponent. For example 2³ involves raising 2 to the power 3, known as “two cubed”.
- Base – the main part of an exponential expression (2 would be the base in the expression 2³).
- Exponent – the power a base is raised to (from the above example 2³, 3 would be the exponent).
- Logarithm – the inverse of exponentiation in the form log
_{b}x. Here, b is the base. *e*– a mathematical constant approximately equal to 2.71828… and the base of the natural logarithm.- Natural logarithm – also known as ln x where
*e*is the base.