Mi niece is in middle school. Over FaceTime today she mentioned she was taking logarithm lessons in math. I was so happy she found them interesting!
She did ask though, “I don’t think I will ever use them though. Why do I need to know what a logarithm is to go buy groceries, for instance?”
I rolled my eyes and told her… well, if you go to the store and find a packaged meal that has a pH of 4 and the next similar meal has a pH of 3, you should know that’s a logarithmic scale with base 10 and the second meal is 10 times more acidic than the first one.
If you go to a rock concert and and the sound engineer is asked to pump the volume up and he increases 10dB, on the scale, that is equivalent to a 10-fold increase in sound intensity (which broadly corresponds with a doubling in loudness). Decibels (sound intensity) is also a logarithmic scale. You ears respond to sound in a logarithmic manner.
If you hear in the news a possible earthquake and they give the intensity in the Richter scale, you should know that, that is also a logarithmic scale. If they announce stronger aftershocks, you should know the Richter scale actually corresponds to the square root of 1000, which is a 31.6 times increase in the energy on the quake. If they announce a Category 5 earthquake and then a 6 one, that one will be 31.6 times stronger… and please, please, please, go to safety…