document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697098>Question 697098</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The intensity level, &#946;, in decibels, of sound is defined as &#946;=10log(I/Io), where I is the instensityof the sound in watts per square metre. The ratioof the intensity of sound pollution measured at a small airport runway versus that of the local highway is 6420,4. If the sound level on the local highway is 91 dB, determine the sound level on the runway. to the nearest decibel.<BR>\n" );
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document.write( "Find the difference in pH levels of a swimming pool with a hydronium ion concentration of 4.4 x 10^(-8) mol/L and a swimming pool with a hydronium ion concentration of 5.7 x 10^(-8) mol/L, to the nearest hundredth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429667 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not understand what was meant by \"the ratio of the intensity of sound pollution measured at a small airport runway versus that of the local highway is 6420,4,\" but I will use my two best guesses.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta=10%2Alog%28%28I%2FI%5Bo%5D%29%29 ALIGN=MIDDLE  ALT=\"beta=10%2Alog%28%28I%2FI%5Bo%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in general, measured by comparison to a reference level of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5Bo%5D ALIGN=MIDDLE  ALT=\"I%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "On the highway, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta%28h%29=10%2Alog%28%28I%5Bh%5D%2FI%5Bo%5D%29%29 ALIGN=MIDDLE  ALT=\"beta%28h%29=10%2Alog%28%28I%5Bh%5D%2FI%5Bo%5D%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "On the runway, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta%28r%29=10%2Alog%28%28I%5Br%5D%2FI%5Bo%5D%29%29=91 ALIGN=MIDDLE  ALT=\"beta%28r%29=10%2Alog%28%28I%5Br%5D%2FI%5Bo%5D%29%29=91\"   DISABLED_style= \"max-width:90%; height:auto;\" >db<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5Br%5D%2FI%5Bh%5D=6420%2F4 ALIGN=MIDDLE  ALT=\"I%5Br%5D%2FI%5Bh%5D=6420%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5Bh%5D%2FI%5Br%5D=4%2F6420%29 ALIGN=MIDDLE  ALT=\"I%5Bh%5D%2FI%5Br%5D=4%2F6420%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta%28h%29=10%2Alog%28%28I%5Bh%5D%2FI%5Bo%5D%29%29=10%2Alog%28%28%28I%5Br%5D%2FI%5Bo%5D%29%28I%5Bh%5D%2FI%5Br%5D%29%29%29=10%2A%28log%28%28I%5Br%5D%2FI%5Bo%5D%29%29%2Blog%28%28I%5Bh%5D%2FI%5Br%5D%29%29%29=10%2Alog%28%28I%5Br%5D%2FI%5Bo%5D%29%29%2B10%2Alog%28%28I%5Bh%5D%2FI%5Br%5D%29%29=91%2B10log%284%2F6420%29=91%2B10%2A%28-3.2%29=91-32=59 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >dB<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5Br%5D%2FI%5Bh%5D=6420.4 ALIGN=MIDDLE  ALT=\"I%5Br%5D%2FI%5Bh%5D=6420.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=I%5Bh%5D%2FI%5Br%5D=1%2F6420.4%29 ALIGN=MIDDLE  ALT=\"I%5Bh%5D%2FI%5Br%5D=1%2F6420.4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=beta%28h%29=91%2B10log%281%2F6420.4%29=91%2B10%2A%28-log%286420.4%29%29=91-10%2A3.8=91-38=53 ALIGN=MIDDLE  ALT=\"beta%28h%29=91%2B10log%281%2F6420.4%29=91%2B10%2A%28-log%286420.4%29%29=91-10%2A3.8=91-38=53\"   DISABLED_style= \"max-width:90%; height:auto;\" >dB<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H ALIGN=MIDDLE  ALT=\"H\"   DISABLED_style= \"max-width:90%; height:auto;\" > = hydronium ion concentration in mol/L<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pH=-log%28H%29 ALIGN=MIDDLE  ALT=\"pH=-log%28H%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pH%5B1%5D=-log%284.4%2A10%5E%28-8%29%29=7.36 ALIGN=MIDDLE  ALT=\"pH%5B1%5D=-log%284.4%2A10%5E%28-8%29%29=7.36\"   DISABLED_style= \"max-width:90%; height:auto;\" > if we round to two decimal places.<BR>\n" );
document.write( "Otherwise <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pH%5B1%5D=7.3565%0D%0A%7B%7B%7BpH%5B2%5D=-log%285.7%2A10%5E%28-8%29%29=7.24 ALIGN=MIDDLE  ALT=\"pH%5B1%5D=7.3565%0D%0A%7B%7B%7BpH%5B2%5D=-log%285.7%2A10%5E%28-8%29%29=7.24\"   DISABLED_style= \"max-width:90%; height:auto;\" > if we round to two decimal places.<BR>\n" );
document.write( "Otherwise <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pH%5B1%5D=7.2441%0D%0ARounding+intermediate+calculations+to+the+same+number+of+decimal+places+would+lead+to+rounding+errors.%0D%0A%7B%7B%7BpH%5B1%5D-pH%5B2%5D=7.3565-7.2441=0.1124=highlight%280.11%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
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document.write( "It could be calculated all at once, without intermediate calculations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pH%5B1%5D-pH%5B2%5D=-log%284.4%2A10%5E%28-8%29%29-%28-log%285.7%2A10%5E%28-8%29%29%29=log%285.7%2A10%5E%28-8%29%29-log%284.4%2A10%5E%28-8%29%29=log%285.7%2A10%5E%28-8%29%2F%284.4%2A10%5E%28-8%29%29%29=log%285.7%2F4.4%29=log%281.295%29=highlight%280.11%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded) </SPAN>\n" );
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