document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=269839>Question 269839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Richter magnitude (m) of an earthquake is given by the formula:\r<BR>\n" );
document.write( "\n" );
document.write( "m = log A/Ao\r<BR>\n" );
document.write( "\n" );
document.write( "(o is subscript for 0)\r<BR>\n" );
document.write( "\n" );
document.write( "where A is the maximum amplitude of the earthquake and Ao is the constant.  What is the magnitude on the Richter scale of an earthquake with an amplitude that is  a million times Ao?\r<BR>\n" );
document.write( "\n" );
document.write( "I know that A=1000000, but am unsure as to what to do with Ao.  There isn't anything about it in my book, so I am unsure as to what to do with this particular logarithmic equation.  Help explaining this would be extremely appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #197682 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=197682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If \"A is the maximum amplitude of the earthquake and Ao is the constant.\" and \"the magnitude on the Richter scale of an earthquake with an amplitude that is a million times Ao\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1000000A%5B0%5D ALIGN=MIDDLE  ALT=\"A=1000000A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=log%28%28A%2FA%5B0%5D%29%29 ALIGN=MIDDLE  ALT=\"m=log%28%28A%2FA%5B0%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > then becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=log%28%281000000A%5B0%5D%2FA%5B0%5D%29%29 ALIGN=MIDDLE  ALT=\"m=log%28%281000000A%5B0%5D%2FA%5B0%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Cancel out the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D ALIGN=MIDDLE  ALT=\"A%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=log%28%281000000%29%29 ALIGN=MIDDLE  ALT=\"m=log%28%281000000%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Afterwards, rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000000 ALIGN=MIDDLE  ALT=\"1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E6 ALIGN=MIDDLE  ALT=\"10%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E6=1000000 ALIGN=MIDDLE  ALT=\"10%5E6=1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" >) to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=log%28%2810%5E6%29%29 ALIGN=MIDDLE  ALT=\"m=log%28%2810%5E6%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, pull down the exponent to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=6log%28%2810%29%29 ALIGN=MIDDLE  ALT=\"m=6log%28%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Finally, evaluate the log of 10 (we're in base 10) to get 1. Ie <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2810%29%29=1 ALIGN=MIDDLE  ALT=\"log%28%2810%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the base is 10.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=6log%28%2810%29%29=6%2A1=6 ALIGN=MIDDLE  ALT=\"m=6log%28%2810%29%29=6%2A1=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In the end, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=6 ALIGN=MIDDLE  ALT=\"m=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the magnitude is 6.0 on the Richter scale. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );