Richter magnitude problem
Date: Wed, 23 Nov 1994 07:36:06 -0800 (PST) From: Marla Friedman Dr.Math- I have been having some problem with the following question and many others like it. I was wondering if you could help me with it. The Richter magnitude, R, of an earthquake is given by R=0.67 log(0.37E)+1.46 where E is the energy in kW*h released by the earthquake. --Show that if R increases by 1 unit, E increases by a factor of about 31. I will appreciate any help you are willing to give me on how to solve this problem. Many Thanks, Marla Friedman
Date: 23 Nov 1994 16:50:26 GMT From: Ken "Dr." Math Organization: The Math Doctors Hello there! This is a problem that's basically about manipulating logarithms. I'll get you started, and then I'll let you take it from there. What we want to do is start with the equation R - 1 = 0.67 Log[0.37 E] + 1.46 And manipulate it until we get something of the form R = 0.67 Log[0.37 X] + 1.46 The X we'll get will be in terms of E. So let's get started. R = 1 + 0.67 Log[0.37 E] + 1.46 R = 0.67(1.49254 + Log[0.37 E]) + 1.46 Now look at the part in the parentheses. We want it to look like the Log of some number, right? Remember the formula Log[a] + Log[b] = Log[ab]? Well, we're going to use that, but first we have to get the 1.49254 into Log form. Can you figure out what the number a is such that Log[a] = 1.49254? Once you've done that, you'll be almost done. I'll let you take it from here. Write back if you have more questions! Ken "Dr." Math
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