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So that we can write general equations, we need to use variables to represent the quantities of interest.
A very important structure, especially in engineering and computer science, and something we need to understand properly before going any further.
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It's common for variables to occur in sequences, so we need notation for that. Then we can perform sum and product operations on them.
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To make notation simpler, we can write a complicated expression in the form of a function.
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The original purpose of logarithms was to convert multiplication into addition (and division into subtraction).
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Storing and computing with very large or small numbers presents difficulties with precision, but logarithms can be used to avoid such problems.
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A demonstration of logarithms in action should help our intuitions at this stage.
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Now we have an intuitive understanding, we can state the formal definition of logarithms.
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From that formal definition, we can state the relationships that enable us to convert multiplication into addition, amongst other things.
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Calculating the logarithm of a number is quite hard, so we use pre-calculated look-up tables.
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