Exponential and Logarithmic Functions

What the resources cover

The page is built around two ideas that undo each other. The mind map Maths Exponents and Logarithms sets this out clearly: inverse operations, then the rules of logs, where multiplication becomes a sum and division becomes a difference. Other maps look at Exponentials, including growth and decay, and Exponential word problems, which covers turning a rate into a decimal and using interest formulas.

Where to start

Begin with a mind map, because it shows the whole topic on one screen. Then move to flashcards to fix the rules in memory.

1. Read Maths Exponents and Logarithms for the inverse link and the log laws.
2. Use Logarithms for the basics, such as what log base 10 means, and for modelling curves with forms like y=kx^n and y=ka^x.
3. Work through the flashcard deck Properties of Logarithms or Log Rules.
4. Check solving methods in Exponential & Logarithmic Functions, which explains matching bases and taking logs of both sides.

Using quizzes and maps together

Take a quiz after each map. Introduction to logs and Logarithm Problems suit a first check. Exponential Growth and Decay tests the word-problem side. The Chapter 4 Quiz mixes inverse functions, converting between log and exponential form, and solving equations. When you miss a question, go back to the matching map branch and read it again.

Several resources mention A-level Maths, including C3 Chapter 3 and the deck C3 e^x and lnx. There are also slides on Logs and Exps Past Paper Questions. Many of the chapter maps come from college algebra and precalculus courses, so they suit university students filling gaps.

Where it fits

This unit sits in the Functions and Graphs strand of Mathematics. It connects naturally with graphing and function work, and the quiz Graphing Exponential Functions shows the link.

Open a map or quiz that matches where you are today, and when you are ready, build your own set of cards to keep the rules close.