Mathematical Logarithms

The huge ranges of seismic wave amplitudes, seismic moments, atmospheric energies, and other physical quantities is a problem. It would be much easier to communicate the energies or moments of earthquakes to the public on a simple scale that just ranges about from one to ten.

To turn these astronomical ranges into a simple scale, we can use the mathematical device of the logarithm. If we raise ten to some power x to make a big number N, then the log of that big number N is the power x:
10^x = N  so  log10(N) = x
Now let's review the log (base 10) of some example numbers:
log10(10)=?; log10(1)=?; log10(100)=2; log10(1e25)=25; log10(25)~1.4; log10(0.01)=-2; log10(-1) is undefined
Note that while you can take the log of a very small number, which will be negative, you can't take the log of any negative number.

J. Louie, revised 29 June 1998

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