document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=49208>Question 49208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: log(4x^2)-log(16x)=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 #32628 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=32628\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%284x%5E2%29-log%2816x%29=1+ ALIGN=MIDDLE  ALT=\"+log%284x%5E2%29-log%2816x%29=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28%284x%5E2%29%2F%2816x%29%29+=+1+ ALIGN=MIDDLE  ALT=\"+log%28%284x%5E2%29%2F%2816x%29%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Assuming the log is base 10, then to remove the log we next to raise both sides to the base 10:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284x%5E2%29%2F%2816x%29+=+10+ ALIGN=MIDDLE  ALT=\"+%284x%5E2%29%2F%2816x%29+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is where the algebraic method and logs seem to me to be at odds to each other. Looking at the above line, we could do one of 2 approaches. Either divide the lefthand side first or move the 16x up to the righthand side.\r<BR>\n" );
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document.write( "Approach1:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%29%2F%284%29+=+10+ ALIGN=MIDDLE  ALT=\"+%28x%29%2F%284%29+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+40+ ALIGN=MIDDLE  ALT=\"+x+=+40+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Approach2:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+=+40x+ ALIGN=MIDDLE  ALT=\"+x%5E2+=+40x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+40x+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+40x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%28x+-+40%29+=+0+ ALIGN=MIDDLE  ALT=\"+x%28x+-+40%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so either x=0 or x-40=0<BR>\n" );
document.write( "--> x=0 or x=40\r<BR>\n" );
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document.write( "This second approach seems to give us 2 answers whereas the first gave us just 1. However, putting x=0 into the original will give you an error, so the only solution is x=40... you must remember to check by substituting your answers back into the question, just to check.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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