document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996322>Question 996322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a question about the logarithmic equations. I'll use log[a, b] where a is the base of the logarithm.\r<BR>\n" );
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document.write( "Is\r<BR>\n" );
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document.write( "log[sqrt3,(1-x)^2] - log[sqrt3, (3-x)] < 2\r<BR>\n" );
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document.write( "equal to\r<BR>\n" );
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document.write( "2 * log[sqrt3, (1-x)] - log [sqrt3, (3-x)]<2\r<BR>\n" );
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document.write( "If they're not equal, why aren't they? Isn't the logarithm property of exponent is log(1-x)^2 = 2 * log(1-x)?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614832 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28sqrt%283%29%2C%281-x%29%5E2%29+-+log%28sqrt%283%29%2C+%283-x%29%29+%3C+2 ALIGN=MIDDLE  ALT=\"log%28sqrt%283%29%2C%281-x%29%5E2%29+-+log%28sqrt%283%29%2C+%283-x%29%29+%3C+2\"   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=log%28sqrt%283%29%2C%281-x%29%5E2%2F+%283-x%29%29+%3C+2 ALIGN=MIDDLE  ALT=\"log%28sqrt%283%29%2C%281-x%29%5E2%2F+%283-x%29%29+%3C+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........change to base <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   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=log%28%281-x%29%5E2%2F+%283-x%29%29%2Flog%28sqrt%283%29%29+%3C+2 ALIGN=MIDDLE  ALT=\"log%28%281-x%29%5E2%2F+%283-x%29%29%2Flog%28sqrt%283%29%29+%3C+2\"   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=log%28%281-x%29%5E2%2F+%283-x%29%29+%3C+2log%28sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"log%28%281-x%29%5E2%2F+%283-x%29%29+%3C+2log%28sqrt%283%29%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=log%28%281-x%29%5E2%2F+%283-x%29%29+%3C+log%28%28sqrt%283%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"log%28%281-x%29%5E2%2F+%283-x%29%29+%3C+log%28%28sqrt%283%29%29%5E2%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=log%28%281-x%29%5E2%2F+%283-x%29%29+%3C+log%283%29 ALIGN=MIDDLE  ALT=\"log%28%281-x%29%5E2%2F+%283-x%29%29+%3C+log%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >....if log same, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-x%29%5E2%2F+%283-x%29+%3C+3 ALIGN=MIDDLE  ALT=\"%281-x%29%5E2%2F+%283-x%29+%3C+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve 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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-x%29%5E2+%3C+3%283-x%29 ALIGN=MIDDLE  ALT=\"%281-x%29%5E2+%3C+3%283-x%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=1-2x%2Bx%5E2+%3C+9-3x ALIGN=MIDDLE  ALT=\"1-2x%2Bx%5E2+%3C+9-3x\"   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=1-2x%2Bx%5E2-9%2B3x%3C0 ALIGN=MIDDLE  ALT=\"1-2x%2Bx%5E2-9%2B3x%3C0\"   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=x%5E2%2Bx-8%3C0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx-8%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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=x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%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=x+=+%28-1+%2B-+sqrt%28+1%2B32+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+1%2B32+%29%29%2F2+\"   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=x+=+%28-1+%2B-+sqrt%28+33+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-1+%2B-+sqrt%28+33+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " exact solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F2%29%28-1+%2B+sqrt%28+33+%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-1+%2B+sqrt%28+33+%29%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=x+=+%281%2F2%29%28-1+-+sqrt%28+33+%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-1+-+sqrt%28+33+%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );