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The change of base formula, log_a x = log_b x / log_b a, rewrites a logarithm in any base — useful for evaluating logs on a calculator and solving equations where the bases differ. It appears across A-Level and iAL Pure Maths with the major exam boards. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Log base a of b equals log of b over log of a in any consistent base. Use it to put an equation into a base your calculator handles, or to combine logs written in different bases.
Before you start
You will want the laws of logarithms at your fingertips first. Getting it right here pays off in solving equations with different bases.
What you learn
Every logarithm you've met so far has kept a single base. This is the last Pure 2 logarithm course. The course works through the change-of-base formula, exact values from a common base, the reciprocal relationship, solving equations with different bases and hidden quadratics via change of base. 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
We teach Changing the Base as one of the Exponentials & Logarithms topics in our A-level course library, at the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. It sits alongside Exponential Functions & Graphs, Exponential Growth & Decay and Introducing Logarithms in the same strand. You can drill this strand further on the Exponentials & Logarithms revision engine, with your accuracy saved to your skill tree.
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