document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93361>Question 93361</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/534494498/algebrahomeworkh>Algebra and Trigonometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The decibel 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 decibel level of a whisper at an intensity of 5.4x 10^-10 watts per square meter. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67990 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=67990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the formula for computing decibels of sound:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%28I%2F%2810%5E-12%29%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%28I%2F%2810%5E-12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "where I is the sound intensity measured in watts per square meter.  The problem tells you<BR>\n" );
document.write( "that a whisper with a sound intensity I of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.4+%2A+10%5E%28-10%29 ALIGN=MIDDLE  ALT=\"5.4+%2A+10%5E%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > watts per square meter takes<BR>\n" );
document.write( "place and asks you to find the decibel level. Begin by substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.4+%2A+10%5E%28-10%29 ALIGN=MIDDLE  ALT=\"5.4+%2A+10%5E%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for I<BR>\n" );
document.write( "in the decibel equation. When you do that the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%28%285.4%2A10%5E-10%29%2F%2810%5E-12%29%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%28%285.4%2A10%5E-10%29%2F%2810%5E-12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The rule for negative integers is that you can change them to a positive integer is the <BR>\n" );
document.write( "quantity is moved from the denominator to the numerator or from the numerator to the denominator.<BR>\n" );
document.write( "In this case move 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;\" > from the denominator and change the exponent to +12.<BR>\n" );
document.write( "This results in the equation becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%28%285.4%2A10%5E-10%29%2A%2810%5E12%29%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%28%285.4%2A10%5E-10%29%2A%2810%5E12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that you have two numbers each having an exponent. Since the two numbers are the same <BR>\n" );
document.write( "(both are 10), you can just raise 10 to the sum of the exponents.  The equation then is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%285.4%2A10%5E%28-10%2B12%29%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%285.4%2A10%5E%28-10%2B12%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which when you combine the exponents by adding them simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%285.4%2A10%5E2%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%285.4%2A10%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E%282%29+=+10%2A10+=+100 ALIGN=MIDDLE  ALT=\"10%5E%282%29+=+10%2A10+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And replacing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2 ALIGN=MIDDLE  ALT=\"10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 100 results in <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%285.4%2A100%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%285.4%2A100%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and 100 times 5.4 equals 540.  This translates the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=+10%2Alog%2810%2C%28540%29%29%29 ALIGN=MIDDLE  ALT=\"D=+10%2Alog%2810%2C%28540%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now using a scientific calculator you can find that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C540%29+=+2.73239376 ALIGN=MIDDLE  ALT=\"log%2810%2C540%29+=+2.73239376\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "you can replace the entire log expression by 2.73239376 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=10%2A2.73239376 ALIGN=MIDDLE  ALT=\"D+=10%2A2.73239376\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and multiplying out the right side gives you the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+27.3239376 ALIGN=MIDDLE  ALT=\"D+=+27.3239376\"   DISABLED_style= \"max-width:90%; height:auto;\" > decibels.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and also helps you to become familiar with <BR>\n" );
document.write( "working with logarithms.<BR>\n" );
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