document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197635>Question 197635</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780618595556/algebrahomeworkh>Texas Edition McDougal Littell Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> CHallenge: Under Certain conditions, the wind speed s (in knots) at an altitude of h meters above a grassy plain can be modeled by this function:<BR>\n" );
document.write( "                  s(h)=2 ln (100h)<BR>\n" );
document.write( "a. By what amount does the wind speed increase when the altitude doubles\r<BR>\n" );
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document.write( "b. Show that the given function can be written in terms of common logarithms as s(h)=2/loge (log h+2)\r<BR>\n" );
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document.write( "umm on a , so far I got change in altitude=s(2h)-s(h)<BR>\n" );
document.write( "then 2ln(100(2h))-2ln(100h) then idk\r<BR>\n" );
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document.write( "on b, i'm not quite sure what to do,  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148198 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=148198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28h%29=2%2Aln%28100h%29 ALIGN=MIDDLE  ALT=\"s%28h%29=2%2Aln%28100h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=2%2Aln%28100%282h%29%29 ALIGN=MIDDLE  ALT=\"s%282h%29=2%2Aln%28100%282h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace \"h\" with \"2h\" (since the altitude doubles)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=2%2Aln%282%2A100h%29 ALIGN=MIDDLE  ALT=\"s%282h%29=2%2Aln%282%2A100h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=2%28ln%282%29%2Bln%28100h%29%29 ALIGN=MIDDLE  ALT=\"s%282h%29=2%28ln%282%29%2Bln%28100h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand the log using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28A%2AB%29=ln%28A%29%2Bln%28B%29 ALIGN=MIDDLE  ALT=\"ln%28A%2AB%29=ln%28A%29%2Bln%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=2%2Aln%282%29%2B2%2Aln%28100h%29 ALIGN=MIDDLE  ALT=\"s%282h%29=2%2Aln%282%29%2B2%2Aln%28100h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=2%2Aln%282%29%2Bs%28h%29 ALIGN=MIDDLE  ALT=\"s%282h%29=2%2Aln%282%29%2Bs%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Aln%28100h%29 ALIGN=MIDDLE  ALT=\"2%2Aln%28100h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28h%29 ALIGN=MIDDLE  ALT=\"s%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Note: this can be done since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28h%29=2%2Aln%28100h%29 ALIGN=MIDDLE  ALT=\"s%28h%29=2%2Aln%28100h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=ln%282%5E2%29%2Bs%28h%29 ALIGN=MIDDLE  ALT=\"s%282h%29=ln%282%5E2%29%2Bs%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the log using the identity  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Aln%28x%29=ln%28x%5Ey%29 ALIGN=MIDDLE  ALT=\"y%2Aln%28x%29=ln%28x%5Ey%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282h%29=ln%284%29%2Bs%28h%29 ALIGN=MIDDLE  ALT=\"s%282h%29=ln%284%29%2Bs%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 2 to get 4\r<BR>\n" );
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document.write( "So when the altitude doubles, the speed of the wind increases by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%284%29 ALIGN=MIDDLE  ALT=\"ln%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > knots. Since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ln(4) \approx 1.38629\">, this means that the speed of the wind increases by about 1.38629 knots.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Are you only supposed to convert to a common log? If so, then there's not much to this part...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28h%29=2%2Aln%28100h%29 ALIGN=MIDDLE  ALT=\"s%28h%29=2%2Aln%28100h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28h%29=2%2Alog%28e%2C%28100h%29%29 ALIGN=MIDDLE  ALT=\"s%28h%29=2%2Alog%28e%2C%28100h%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert to a standard log of base \"e\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28h%29=2%2A%28log%2810%2C%28100h%29%29%2Flog%2810%2C%28e%29%29%29 ALIGN=MIDDLE  ALT=\"s%28h%29=2%2A%28log%2810%2C%28100h%29%29%2Flog%2810%2C%28e%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now use the change of base formula (this step may be optional)\r<BR>\n" );
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document.write( "Remember the change of base formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29 ALIGN=MIDDLE  ALT=\"log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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