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Name: Alan
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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 logarithmic functions.

Dr. Mellendorf

Like this:

10 = 398107170.6

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:

Vince Calder

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