document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138533>Question 1138533</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The intensity levels I of two earthquakes measured on a seismograph can be compared by the formula log(I1/I2)= M1 - M2<BR>\n" );
document.write( "where M is the magnitude given by the Richter scale. An earthquake of magnitude 6.9 hit a city. Two years later, that same region experienced yet another, more devastating earthquake, this time with a magnitude of 9.0. How many times greater was the intensity of the second earthquake? Round to the nearest whole number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756337 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=756337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9.0 = log(M1) if and only if 10^9 = M1.\r<BR>\n" );
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document.write( "6.9 = log(M2) if and only if 10^6.9 = M2.\r<BR>\n" );
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document.write( "M1 / M2 = 10^9 / 10^6.9 = 10^(9 - 6.9) = 10^2.1  which means that M1 = 10^2.1 times as powerful as M2 which means that M1 = 125.8925412 times as powerful as M2.\r<BR>\n" );
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document.write( "the logarithmic scale works this way.\r<BR>\n" );
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document.write( "log(x) = y if and only if y = 10^x.\r<BR>\n" );
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document.write( "that's if the logarithmic scale is to the base of 10, which it is when you are dealing with the richter scale.\r<BR>\n" );
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document.write( "when applied to magnitudes of earthquakes, y is the magnitude of the earthquake and x is the intensity or the earthquake, or the amount of energy released by the earthquake.\r<BR>\n" );
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document.write( "an earthquake with a magnitude of 7 will be 10 times as powerful as earthquake with a magnitude of 6, based on the richter scale.\r<BR>\n" );
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document.write( "the magnitude of 7 will be related to the intensity by the formula y = log(x) where y is the magnitude and x is the intensity.\r<BR>\n" );
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document.write( "the intensity is a relative measure to earthwuakes of different magnitudes.\r<BR>\n" );
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document.write( "a magnitude 7 will be related to intensity by the formula 7 = log(x1).\r<BR>\n" );
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document.write( "a magnitude 6 will be related to intensity by the formula 6 = log(x2)\r<BR>\n" );
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document.write( "the log function is the inverse of the exponent function.\r<BR>\n" );
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document.write( "7 = log(x1) if and only if 10^7 = x1.\r<BR>\n" );
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document.write( "6 = log(x2) if and only if 10^6 = x2.\r<BR>\n" );
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document.write( "x1 is x1/x2 times as powerful as x2 = 10^7 / 10^6 = 10 times as powerful.\r<BR>\n" );
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document.write( "these measures are, by themselves, very simplistic and don't take into account the many factors that are used to measure the overall strength of an earthquake, but are a good basic definition of the relationship between magnitude and intensity on the richter scale.\r<BR>\n" );
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document.write( "the main point here is that the richter scale is a logarithmic scale and that every integer higher on the richter scale means that the power of the earthquake is 10 times as much as the next integer lower.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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