I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...

OpenAI has added visual explanations to ChatGPT, allowing users to manipulate formulas and more s in real time to better understand complex concepts.

Katie has a PhD in maths, specializing in the intersection of dynamical systems and number theory. She reports on topics from maths and history to society and animals. Katie has a PhD in maths, ...