document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203500>Question 203500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can someone help me with this question<BR>\n" );
document.write( "thanx.\r<BR>\n" );
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document.write( "solve the following equation for x, giving the answer correct to two decimal places\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x-2%29=2%5E%28x%2B3%29 ALIGN=MIDDLE  ALT=\"5%5E%28x-2%29=2%5E%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "this question is from the book Longman Pre-U Text STPM Mathematics S & T Paper 1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153526 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=153526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve for x when it is in exponents is to use logarithms. Since we want our answer in decimal form (and not logarithm form) we need to use a logarithm we can get from out calculator (or other computing device). If calculators have any logarithms at all they will most likely have base 10 logarithms and/or natural (base e) logarithms. Either will work and give the correct answer to the problem.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%28x-2%29=2%5E%28x%2B3%29 ALIGN=MIDDLE  ALT=\"5%5E%28x-2%29=2%5E%28x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the log of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%285%5E%28x-2%29%29%29=log%28%282%5E%28x%2B3%29%29%29 ALIGN=MIDDLE  ALT=\"log%28%285%5E%28x-2%29%29%29=log%28%282%5E%28x%2B3%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can get x out of the exponents by using the following property of logarithms (which applies to all bases): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28a%5Eb%29%29+=+b%2Alog%28%28a%29%29 ALIGN=MIDDLE  ALT=\"log%28%28a%5Eb%29%29+=+b%2Alog%28%28a%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Applying this to our logarithms we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2Alog%28%285%29%29=%28x%2B3%29%2Alog%28%282%29%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%2Alog%28%285%29%29=%28x%2B3%29%2Alog%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%285%29%29%29x+-+2log%28%285%29%29+=+%28log%28%282%29%29%29x+%2B+3log%28%282%29%29 ALIGN=MIDDLE  ALT=\"%28log%28%285%29%29%29x+-+2log%28%285%29%29+=+%28log%28%282%29%29%29x+%2B+3log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We are now in a position to solve for x. We can either<ul><li>replace the logarithms now with decimals and finish the solution with these decimals</li><li>Or, complete the solution with logarithms and replace them with decimals at the end.</li></ul><BR>\n" );
document.write( "I will use the second approach. But if you can't understand this, then repalce the logarithm's now and finish the solution using the decimals.<BR>\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%282%29%29%29x ALIGN=MIDDLE  ALT=\"%28log%28%282%29%29%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%285%29%29+-+log%28%282%29%29%29x+-+2log%28%285%29%29+=+3log%28%282%29%29 ALIGN=MIDDLE  ALT=\"%28log%28%285%29%29+-+log%28%282%29%29%29x+-+2log%28%285%29%29+=+3log%28%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%28%285%29%29 ALIGN=MIDDLE  ALT=\"2log%28%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%285%29%29+-+log%28%282%29%29%29x+=+3log%28%282%29%29+%2B+2log%28%285%29%29 ALIGN=MIDDLE  ALT=\"%28log%28%285%29%29+-+log%28%282%29%29%29x+=+3log%28%282%29%29+%2B+2log%28%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log%28%285%29%29+-+log%28%282%29%29%29 ALIGN=MIDDLE  ALT=\"%28log%28%285%29%29+-+log%28%282%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%283log%28%282%29%29+%2B+2log%28%285%29%29%29%2F%28log%28%285%29%29+-+log%28%282%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We can get the logarithms above from our calculator:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%283%280.3010299956639812%29+%2B+2%280.6989700043360188%29%29%2F%28%280.6989700043360188%29+-+%280.3010299956639812%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying gives:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5.7823539868301501 ALIGN=MIDDLE  ALT=\"x+=+5.7823539868301501\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rounded to 2 decimal places:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5.78 ALIGN=MIDDLE  ALT=\"x+=+5.78\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );