Why do we learn logarithms in a modern era of computers?
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Are you asking why we use them outside of computation, which we no longer need them for?
There are lots of applications and a big one is optimization.
Basically, say we have some expression we wish to optimize – find the maximum or minimum of. There are well known ways to do this via calculus… but in many cases they become easier if we instead optimize the logarithm of that expression.
This is because logarithms turn products into addition which are easier to work with. And since log is an increasing function, optimizing the log of an expression is the same as optimizing the expression itself.
Lots of the current work in deep learning/AI for example is built, essentially, on optimizing expressions involving logarithms. Programming this requires understanding the underlying optimization problem and that includes being able to manipulate logarithms.
But that’s just one examples. There are many others in theoretical or applied math.
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