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Richter Scale Exponents
Name: Alan
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
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?
Replies:
Alan,
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
logarithmic functions.
Dr. Mellendorf
Like this:
x
10 = 398107170.6
x
log(10 ) = log(398107170.6)
x * log(10) = log(398107170.6)
x * 1 = log(398107170.6)
x = 8.6
Tim Mooney
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
website:
http://www.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.html
Vince Calder
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Update: June 2012
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