document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72681>Question 72681</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The decible level of sound is given by D=10 log (I/10^-12, where I is the sound intensity measured in watts per square meter. Find the decible level of a whisper at an intensity of 5.4 ? 10-10 watts per meter.\r<BR>\n" );
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document.write( "Does anyone understand this? If so please break it down for me.  Thanks to anyone who can help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52054 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=52054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since nobody else has taken a shot at this, I'll give it a go ...<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB+=+10%2Alog%28%28I%2F10%5E%28-12%29%29%29 ALIGN=MIDDLE  ALT=\"dB+=+10%2Alog%28%28I%2F10%5E%28-12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "is the equation that governs the relationship between sound intensity and decibels.<BR>\n" );
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document.write( "I think what you meant for the given sound intensity was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.4%2A10%5E%28-10%29 ALIGN=MIDDLE  ALT=\"5.4%2A10%5E%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The units of your given intensity and the units of the intensity in the decibel equation <BR>\n" );
document.write( "are consistent, so we can just substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.4%2A10%5E%28-10%29 ALIGN=MIDDLE  ALT=\"5.4%2A10%5E%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for I in the decibel<BR>\n" );
document.write( "equation without having to make any conversion in units.  With this substitution the decibel <BR>\n" );
document.write( "equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB+=+10%2Alog%28%285.4%2A10%5E%28-10%29%2F10%5E%28-12%29%29%29 ALIGN=MIDDLE  ALT=\"dB+=+10%2Alog%28%285.4%2A10%5E%28-10%29%2F10%5E%28-12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We can now divide the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%28-12%29 ALIGN=MIDDLE  ALT=\"10%5E%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the denominator into the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%28-10%29 ALIGN=MIDDLE  ALT=\"10%5E%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the <BR>\n" );
document.write( "denominator.  Recall that when you divide, you subtract exponents.  The subtraction<BR>\n" );
document.write( "of the exponents involves <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10%29-%28-12%29 ALIGN=MIDDLE  ALT=\"%28-10%29-%28-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10%2B12+=2 ALIGN=MIDDLE  ALT=\"-10%2B12+=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore,<BR>\n" );
document.write( "the decibel equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB+=+10%2Alog%28%285.4%2A10%5E%282%29%29%29 ALIGN=MIDDLE  ALT=\"dB+=+10%2Alog%28%285.4%2A10%5E%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The rules of logarithms say that if you have the log of a product, you can split this into<BR>\n" );
document.write( "the sum of the logs of each of the terms in the product.  Applying this rule gives us:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB+=+10%2A%28log%28%285.4%29%29+%2B+log%28%2810%5E%282%29%29%29%29 ALIGN=MIDDLE  ALT=\"dB+=+10%2A%28log%28%285.4%29%29+%2B+log%28%2810%5E%282%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The rule of exponents for logarithms says that an exponent comes out as the multiplier <BR>\n" );
document.write( "of the log.  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28%2810%5E%282%29%29%29 ALIGN=MIDDLE  ALT=\"log+%28%2810%5E%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Alog+%28%2810%29%29 ALIGN=MIDDLE  ALT=\"2%2Alog+%28%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2810%29%29 ALIGN=MIDDLE  ALT=\"log%28%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is simply 1,<BR>\n" );
document.write( "and therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%2810%5E%282%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%2810%5E%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > reduces just to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Substitute this back into the <BR>\n" );
document.write( "decibel equation and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB+=+10%2A%28log%28%285.4%29%29+%2B+2%29 ALIGN=MIDDLE  ALT=\"dB+=+10%2A%28log%28%285.4%29%29+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finding the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285.4%29%29 ALIGN=MIDDLE  ALT=\"log%28%285.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is just a calculator problem.  It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.732393759 ALIGN=MIDDLE  ALT=\"0.732393759\"   DISABLED_style= \"max-width:90%; height:auto;\" > or just  round it<BR>\n" );
document.write( "to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.732 ALIGN=MIDDLE  ALT=\"0.732\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is probably close enough for your needs.  <BR>\n" );
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document.write( "Substituting this value makes the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dB+=+10%2A%280.732+%2B+2%29+=+10%2A2.732+=+27.32+ ALIGN=MIDDLE  ALT=\"dB+=+10%2A%280.732+%2B+2%29+=+10%2A2.732+=+27.32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer appears to be 27.32 dB<BR>\n" );
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document.write( "Hope you could follow this through and that it helps you to understand this power ratio<BR>\n" );
document.write( "equation. </SPAN>\n" );
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