document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80892>Question 80892</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ASAP HELP!(^)I use this symbol to represent exponents\r<BR>\n" );
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document.write( "I have a question, if the loudness level of a sound, D, in decibels, is given by the formula D= 10 log (10^12 I) where I is the intensity of the sound, in watts per meter^2. Decibel levels range from 0, a barely audible sound, to 160, a sound resulting in a ruptured eardrum. What is the decibel level of a normal conversation, 3.2 x 10^-6 watt per meter^2?\r<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 #58042 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=58042\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If your decibel formula is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 \log_{10}(10^{12} I)\">\r<BR>\n" );
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document.write( "Simply plug in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large I=3.2x10^{-6}\"> into I\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 \log_{10}(10^{12}(3.2x10^{-6}))\">\r<BR>\n" );
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document.write( "Group the terms <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 10^{12}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large 10^{-6}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 \log_{10}(10^{12}(10^{-6})(3.2))\">\r<BR>\n" );
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document.write( "Since we're multiplying two like bases with exponents we can add the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 \log_{10}(10^{12+(-6)}(3.2))\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 \log_{10}(10^{6}(3.2))\"> add the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 (\log_{10}(10^{6})+\log_{10}(3.2))\"> Break up the logs by using this identity <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \log(x*y)=\log(x)+\log(y)\">\r<BR>\n" );
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document.write( "We can clearly see that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \log_{10}(10^{6})=6\"> (since this is always true <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \log_{10}(10^{x})=x\">) so it reduces to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 (6+\log_{10}(3.2))\">\r<BR>\n" );
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document.write( "Now use your calculator to find <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \log_{10}(3.2)\">. It comes to 0.50515\r<BR>\n" );
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document.write( "So our problem reduces further to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 (6+0.50515)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 10 (6.50515)\"> Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large D= 65.0515\"> Multiply\r<BR>\n" );
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document.write( "So an intensity of 3.2 x 10^-6 watt per meter^2 means the decibel measure is about 65.015 decibels. For more problems dealing with decibels check out this <a  rel=nofollow HREF=\"http://www.sengpielaudio.com/calculator-soundlevel.htm\"> decibel calculator</a>. You'll need to use the calculator on the far right. </SPAN>\n" );
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