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I am both a Mechanical and an Electrical engineer ( aka use math in real life every day) and I work every day with systems described by exponential or logarithmic functions.

Just to name a few:

  • Charging or discharging of a capacitor
  • Any LRC circuit (or any combination thereof)
  • Any SMD system (or any combination thereof)
  • radioactive decay
  • algorithmic efficiency

In other words, if you want to describe a real life you will probably encounter some exponential function. This comes from the fact that the solution to differential equations ( which govern most of the universe) generally contain an exponential term.

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Q: How do you use logarithmic functions in real life?
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