Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne 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



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory