document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189074>Question 1189074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> B. The strength of an earthquake is calculated using Richter's formula M= log (A/10^-6) where A is the seismograph amplitude of the earthquake measured in meters.<BR>\n" );
document.write( "1. If the earthquake has a seismograph amplitude ot 10^-3 m, find the magnitude of the earthquake.<BR>\n" );
document.write( "2. The magnitude of the earthquake that hit the Central Visayas in 2013 is 7.2 on the Richter scale. What is the seismograph amplitude of the earthquake?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820301 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=820301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula given is:\r<BR>\n" );
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document.write( "m = log (a / 10^-6) where a is the amplitude and m is the magnitude.\r<BR>\n" );
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document.write( "if the amplitude is 10^-3, then the formula becomes:\r<BR>\n" );
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document.write( "m = log(10^-3 / 10^-6) = log(10^-3+6)) = log(10^3) = 3\r<BR>\n" );
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document.write( "if m = 7.2, then 7.2 = log(a / 10^-6)\r<BR>\n" );
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document.write( "this becomes 7.2 = log(a) - log(10^-6) which becomes 7.2 = log(a) - -6 * log(10) which becomes 7.2 = log(a) + 6 * log(10) which becomes 7.2 = log(a) + 6.\r<BR>\n" );
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document.write( "subtract 6 from both sides of the eqution to get:\r<BR>\n" );
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document.write( "7.2 - 6 = log(a)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "1.2 = log(a)\r<BR>\n" );
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document.write( "this is true if and only if 10^1.2 = a\r<BR>\n" );
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document.write( "sove for a to get:\r<BR>\n" );
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document.write( "a = 15.84893192.\r<BR>\n" );
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document.write( "that should be the amplitude.\r<BR>\n" );
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document.write( "confirm by replacing a in the original equation by that to get:\r<BR>\n" );
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document.write( "7.2 = log(a / 10^-6) becomes 7.2 = log(15.84893192 / 10^-6) = 7.2.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "some log properties that were used.\r<BR>\n" );
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document.write( "log(a/b_)  log(a) - log(b)\r<BR>\n" );
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document.write( "y = log(x) if and only if 10^y = x\r<BR>\n" );
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document.write( "and:\r<BR>\n" );
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document.write( "10^x = y if and only if log(y) = x\r<BR>\n" );
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document.write( "log(x) means the same as log10(x).\r<BR>\n" );
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document.write( "log10(x) means the log of b to the base of 10.\r<BR>\n" );
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document.write( "log10 is the log function on your calculator.\r<BR>\n" );
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document.write( "the general equation is:\r<BR>\n" );
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document.write( "loga(b) = c if and only if a^c = b\r<BR>\n" );
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document.write( "in reverse, a^c = b if and only if loga(b) = c\r<BR>\n" );
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document.write( "there is also a log base conversion formula that says.\r<BR>\n" );
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document.write( "loga(x) = logb(x) / logb(a)\r<BR>\n" );
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document.write( "this is useful to convert logs of any base to the base of 10 which is the log function of your calculator.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "log2(16) = y if and only if 2^y = 16<BR>\n" );
document.write( "solve for y to get y = 4 because 2^4 = 16.\r<BR>\n" );
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document.write( "using the base conversion formula, you could also have done:<BR>\n" );
document.write( "log2(16) = log(16)/log(2) = 4 by using the log function of your calculator.\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( "here's some references.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/\" target = \"_blank\">https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.storyofmathematics.com/logarithm-rules\" target = _blank\">https://www.storyofmathematics.com/logarithm-rules</a><BR>\n" );
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