Richter Scale Exponents
The Richter Scale yields very large numerical
values from powers of base 10.
If know that the value is equal to an exponent of base ten, how do I
calculate the exponent without factoring the numerical value by 10?
Example: 10 to the 8.6 power equals 398107170.6.
10 to the X power equals 398107170.6. How do I find X without factoring?
There is a special function to do this called a logarithm. A calculator has
two such functions. One is base 10, called the common log and expressed as
"log". If 10^x=123456, then x=log(123456). The other is base e, called the
natural logarithm and expressed as "ln". "e" is a number, e=2.71828....
If e^x=54321, then x=ln(54321).
The special property of "e" relates to slope. If you graph the function
y=e^x, the slope of the graph will exactly equal the value of the graph
everywhere. In higher mathematics, such as calculus and differential
equations, this is a very important function. This is why scientific
calculators have both base 10 and base "e" for their exponential and
10 = 398107170.6
log(10 ) = log(398107170.6)
x * log(10) = log(398107170.6)
x * 1 = log(398107170.6)
x = 8.6
The Richter scale is a logrithmetric scale for measuring the energy
of an earthquake, you are correct. However, it is a bit more
complicated than that. simply looking up the log (398107170.6) in a
table or on a calculator. It involves several factors that
contribute to an earthquake's energy. The details are too long to go
into in a short forum like NEWTON but are discussed in detail on the
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Update: June 2012