Feel the Earth Shake

2 Jun

The Richter Scale is a base 10 logarithmic scale used to measure the strength of earthquakes. A 5.0 earthquake moves the Earth 10^5 microns.

So lets solve this 5x = 212

Since 212 is not a power of 5, then I will have to use logs to solve this equation. I could take base-5 log of each side, solve, and then apply the change-of-base formula, but I think I’d rather just use the natural log in the first place:

5x = 212

ln(5x) = ln(212)

x · ln(5) = ln(212)

x=ln(212)ln(5)x=ln(5)ln(212)

…or about 3.328, rounded to three decimal places.

How else can an earthquake be measured?

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