Logarithms intimidate everyone in high school. They are also the single most useful tool for measuring sound, earthquakes, growth and decay.
This used to be a back-of-the-envelope job. Now it is one tap, but the logic has not changed. Logarithms intimidate everyone in high school. They are also the single most useful tool for measuring sound, earthquakes, growth and decay.
log₁₀(1000) = 3, because 10³ = 1000. A log is just 'how many times must I multiply the base?'
Each whole number on the scale is 10× more shaking. Magnitude 7 is 10× a magnitude 6.
10 dB difference = 10× sound intensity. 70 dB to 80 dB doubles loudness.
Doubling time = ln(2) / growth rate. Used in compound interest and biology.
Why is log so useful? It turns multiplication into addition — slide rules and the entire pre-calculator engineering world ran on this.
What does log on a regular calculator mean? Usually base 10. 'ln' is natural log (base e).
Bookmark the calculator linked above — you will need it more often than you think.