Why do we learn logarithms in a modern era of computers?
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The logarithm is a common and useful mathematical function that shows up in a ton of different places. Logarithms aren’t just there for slide rules. They show up as a common integral in calculus (integral du/u = ln(u) + C) and thus in the solution to a very common type of differential equation. They show up when solving any equation involving a variable in an exponent, as with things like half-lives, decay constants, or continuously compounding interest. A full list of everywhere they appear would be quite long.
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