Pattern, Exception, and Update
Hello mathematicians, puzzlers, and other curious people! Due to speedbumps, instead of all content in Gap Year Math units being available on launch day, the first lessons of each will be up and the rest will roll out over about 1-2 weeks. It was that or push back the launch, and I want people to have the option to start as soon as they want to! It\’ll be a while before we get to the units on logarithms, but since we will eventually, that ties in well with something that came up recently on a math discussion group on Facebook: a student had been told that when a log function\’s input is less than the base, such as 
, the value is a fraction, such as 1/2. This makes a certain amount of sense because log functions are increasing and 
, so if the input is less than the base, the output should be less than 1, like a fraction. They tried out different things and seeing what happened (which is a very valid investigation technique) and found something different. When the input is a fraction, like 
in 
, the output turns out to be a negative number, like -2. The student who noticed this wanted to know why. We talked it over and they figured it out, and I\’m definitely going to include this topic in the Gap Year Math units on logarithms. Feel free to talk it over in the comments section in the meantime. Calc You Later!
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