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

In this paper we derive the explicit, closed-form, recursion-free formulae for the arbitrary-order Fréchet derivatives of the exponential and logarithmic functions in unital Banach algebras (complex ...

This is a preview. Log in through your library . Abstract We generalize the Newton polygon procedure for algebraic equations to generate solutions of polynomial differential equations of the form ∑∞ ...

The purpose of all of the developmental mathematics courses is to support student success academically and beyond by advancing critical thinking and reasoning skills. Specifically in Algebra II, as a ...

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 ...

Microsoft is making solving mathematic problems a little easier. The Redmond-headquartered technology giant has introduced an AI-based Math Solver application that can be used to solve math problems ...

Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms, we can ...