Exponentials and Logarithms

DfE content area F: the functions a^x and e^x, logarithms as their inverses, and how to use them to solve equations and model growth and decay.

• An Overview — the big idea, the language, the five core techniques and the common mistakes

The content statements

• Exponential Functions and e — graphs of a^x, the number e, the gradient of e^kx, and ln x as the inverse of e^x
• Logarithms and Their Laws — the definition, the three laws, natural logs, and switching between index and log form
• Exponential and Log Equations — solving a^x = b, hidden quadratics in e^x or 2^x, and equations involving logs
• Exponential Modelling — growth and decay models, reduction to linear form, and the limitations of models

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.