**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 5^{x} = 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:

5^{x} = 212

ln(5^{x}) = ln(212)

*x · *ln(5) = ln(212)

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

…or about 3.328, rounded to three decimal places.

How else can an earthquake be measured?