\({\log _a}a = 1\) (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 ...

This video explains a challenging exponential equation step by step, showing how to simplify expressions, apply exponent rules, and solve systematically without skipping key logic. Perfect for ...

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, ...

What are the underlying principles of how populations change over time? Two basic principles are involved, the idea of exponential growth and its ultimate control. The basics of population ecology ...