document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969599>Question 969599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The decibel level of a sound with intensity x watts per square centimeter is given by the formula D= 10 log(10^16x).<BR>\n" );
document.write( "a) Normal conversation is about 60 decibels. What is the sound intensity of normal conversation?<BR>\n" );
document.write( "b) A loud car is 85 decibels. How many times more intense is the loud car than normal conversation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592425 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start with 60 db\r<BR>\n" );
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document.write( "60=10 log(10^16x)<BR>\n" );
document.write( "Divide both sides  by 10<BR>\n" );
document.write( "6=log (10^16x)<BR>\n" );
document.write( "raise each to the power of 10.  That removes the log.  Furthermore, 10 ^log x=x.  e^ln x=x.  They are opposites just like multiplication and division are.  Therefore, 10^{log 10^16x}=10^16x<BR>\n" );
document.write( "10^6=10^16x\r<BR>\n" );
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document.write( "Divide by 10^16.\r<BR>\n" );
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document.write( "(10^6/10^16)=x <BR>\n" );
document.write( "x= 10^(-10)  because when you divide, you subtract exponents.  6-16=-10  <BR>\n" );
document.write( "x=10^(-10) watts/sq meter.\r<BR>\n" );
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document.write( "For 85 decibels\r<BR>\n" );
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document.write( "85=10 log (10^16x)<BR>\n" );
document.write( "Divide by 10<BR>\n" );
document.write( "8.5=log (10^16x)\r<BR>\n" );
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document.write( "10^8.5=10^16x.  Don't try to get a specific number for 10^8.5 yet.  <BR>\n" );
document.write( "Divide by 10^16, both sides\r<BR>\n" );
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document.write( "x=10^(-7.5)\r<BR>\n" );
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document.write( "Still don't get a specific number.  Leave it as is for now.\r<BR>\n" );
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document.write( "The louder is divided by the smaller, so we divide 10^(-7.5)/ 10^(-10)\r<BR>\n" );
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document.write( "Moving the negative exponent to the top makes it positive, so (-7.5+10)=2.5\r<BR>\n" );
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document.write( "The louder is 10^2.5 times louder than the smaller.  That answer is not unreasonable in that form, but most would want a specific ratio, not a power of 10. NOW you can raise 10^2.5 to get 316.2, which is how much louder 85 dB is than 60 dB.\r<BR>\n" );
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document.write( "Notice that decibels from 60 to 85 will be 10^[(85-60)/10] times louder.  <BR>\n" );
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