Remember one of the laws of logs: \(n{\log _a}x = {\log _a}{x^2}\) Another one of the laws are used here: \({\log _a}x + {\log _a}y = {\log _a}xy\) ...

A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division. Laws of logarithms and exponents Revise what logarithms are and how to use ...

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 ...

We derive estimates on the magnitude of non-adiabatic interaction between a Hamiltonian partial differential equation and a high-frequency nonlinear oscillator. Assuming spatial analyticity of the ...