document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24059>Question 24059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP ME SOLVE THIS PROBLEM.<BR>\n" );
document.write( "Logbase3(1+x)>(1-Logbasex(1-x))Logbase3x.<BR>\n" );
document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12826 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=12826\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <p>Sorry, about the slightly messy notation, but I'm still trying to figure out how to use this thing.</p>\r<BR>\n" );
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document.write( "<p>Ok, I assume the thing that's making it tricky for you is the rather nastly looking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lg%5Bx%5D ALIGN=MIDDLE  ALT=\"lg%5Bx%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. When I first saw this problem I thought eugh! What on earth am I going to do with that. I then remembered somebody's (probably not) famous theorem.</p>\r<BR>\n" );
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document.write( "<p>Logs of different bases differ by a multiplicitive constant!</p>\r<BR>\n" );
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document.write( "<p>Let me demonstrate this with an example, say we wanted to solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%5Ex=29.6 ALIGN=MIDDLE  ALT=\"14%5Ex=29.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I'm sure you could tell me straight away that the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=lg%5B14%5D%2829.6%29 ALIGN=MIDDLE  ALT=\"x=lg%5B14%5D%2829.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. But let's try and work out the answer another way. Lets take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lg%5B10%5D ALIGN=MIDDLE  ALT=\"lg%5B10%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > of both sides of the equation.</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lg%5B10%5D%2814%5Ex%29=lg%5B10%5D%2829.6%29 ALIGN=MIDDLE  ALT=\"lg%5B10%5D%2814%5Ex%29=lg%5B10%5D%2829.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>Applying one of the many \"laws of logs\"</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alg%5B10%5D%2814%29=lg%5B10%5D%2829.6%29 ALIGN=MIDDLE  ALT=\"x%2Alg%5B10%5D%2814%29=lg%5B10%5D%2829.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>And finally dividing<p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=lg%5B10%5D%2829.6%29%2Flg%5B10%5D%2814%29 ALIGN=MIDDLE  ALT=\"x=lg%5B10%5D%2829.6%29%2Flg%5B10%5D%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>So, we've solved for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in two different ways, and thus we have worked out that</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lg%5B14%5D%2829.6%29=lg%5B10%5D%2829.6%29%2Flg%5B10%5D%2814%29 ALIGN=MIDDLE  ALT=\"lg%5B14%5D%2829.6%29=lg%5B10%5D%2829.6%29%2Flg%5B10%5D%2814%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>Now if you can do the same thing and turn the nasty <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lg%5Bx%5D ALIGN=MIDDLE  ALT=\"lg%5Bx%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > into a much nicer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lg%5B3%5D ALIGN=MIDDLE  ALT=\"lg%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > you should be able to do the problem.</p>\r<BR>\n" );
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document.write( "<p>There is another possibly tricky bit, but see how you get on. please write back if you didn't follow that, or you get stuck further on.</p>\r<BR>\n" );
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document.write( "<p>Hope that helps</p>\r<BR>\n" );
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document.write( "<p>Kev</p> </SPAN>\n" );
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