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When the unknown is in the power, such as 3ˣ = 20, logarithms bring it down to solve. This topic covers taking logs of both sides, applying the laws of logarithms and solving exponential equations. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Take logs of both sides, then bring the power down in front. Solve the resulting linear equation and check the answer is valid — logs of negative numbers do not exist, so some solutions must be rejected.
Before you start
Check the laws of logarithms first if this feels hard. Later work on growth and decay problems assumes it. It belongs to the Pure 2 specification.
What you learn
Either base works on the calculator — just be consistent. The course works through taking logs of both sides, when the exponent is a linear expression, hidden quadratics in a^x, isolate the power, or logs on both sides and solving logarithmic equations. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Solving Equations Using Logarithms is a Exponentials & Logarithms topic in the A-level syllabus, covered here at the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Nearby topics in the same strand are Changing the Base, Exponential Functions & Graphs, Exponential Growth & Decay, Introducing Logarithms and Laws of Logarithms. You can drill this strand further on the Exponentials & Logarithms revision engine, with your accuracy saved to your skill tree.
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