Logs are one of the easiest topics to find examples to use when asked by students "When will I ever use this?" Without thinking about it, I can come up with:
1. Richter Scale.
2. Population growth or decrease.
3. Half - Life.
4. Continuous Interest.
These are the usual types of problems I find in the problems sections of text books but what are the other uses of logs and natural logs in real life. Ways we might not think about as we are trying to convince students that math is used outside of the classroom.
1. It turns out that decibel levels are log based.
2. Newtons law of cooling - This is concept is used to figure out the change in temperature when an item is taken from one temperature and placed in a place with a different temperature.
T = e^kt+C + R
3. Calculating the monthly mortgage payment.
4. The ph scale for acids and bases -
pH = − log [H3O+]
5. Carbon dating which makes sense because of half life decay.
6. Finance - interest rates, stock prices, and value of currency.
7. Benford's Law which looks at frequency distribution of digits in data. It is applied to street addresses, stock prices, and death rates.
8. Tones and intervals in music and sound intensity.
So eight more ways logs and natural logs are used in real life. It would make a really good short project in upper level maths, to have students research each use and them create part of a presentation so the final presentation would include all 8 ways.
I actually was unaware of a couple of these so even I've learned something. Great.