When logarithms are first introduced at AS level, students often find the concept baffling. This is not helped when the topic is often delivered with exams approaching and learning can feel rushed. Discovery of logarithms is credited to Scottish mathematician John Napier in 1614, so they've been around for 400 years or so, waiting to be studied at A level.
Logarithms are a powerful tool in the mathematician's toolkit. For example they allow us to solve equations where the unknown is in the power or index. They are also very helpful in modelling non-linear relationships between two variables. The Richter-scale for measuring the size of an earthquake is an example of a logarithmic or exponential scale, in base 10. On the Richter-scale, each successive order of magnitude is 10 times larger than the previous, so magnitude 2 is 10 times more than magnitude 1 and magnitude 3 is 10 times more again.
At A level, there are various processes to learn, equations to be solved, laws of logs to be applied. However, many students fail to understand adequately what a logarithm is, and how it fits into our understanding of the number system. If you can visualise the fundamental relationship between powers and logs, then you are likely to be more successful and efficient when solving new problems. Here's a little dynamic I've just created to illustrate what a logarithm is, and how it is related to powers (or exponents).
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