document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4558>Question 4558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve problem exactly\r<BR>\n" );
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document.write( "ln (x + 1) = ln (3x + 1)- ln x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2090 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2090\">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=ln+%28x%2B1%29+=+ln+%283x+%2B+1%29+-+ln+%28x%29 ALIGN=MIDDLE  ALT=\"ln+%28x%2B1%29+=+ln+%283x+%2B+1%29+-+ln+%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "By the second law of logarithms, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+M+-+ln+N+=+ln+%28M%2FN%29 ALIGN=MIDDLE  ALT=\"ln+M+-+ln+N+=+ln+%28M%2FN%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%28x%2B1%29+=+ln+%28%283x+%2B+1%29%2Fx%29+ ALIGN=MIDDLE  ALT=\"ln+%28x%2B1%29+=+ln+%28%283x+%2B+1%29%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, since there are ln s on both sides of the equation, raise both sides as a power of e:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28ln%28x%2B1%29%29+=+e%5E+%28ln+%28%283x+%2B+1%29+%2F+x%29%29+ ALIGN=MIDDLE  ALT=\"e%5E%28ln%28x%2B1%29%29+=+e%5E+%28ln+%28%283x+%2B+1%29+%2F+x%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+%2B+1+=+%283x+%2B+1%29+%2F+x ALIGN=MIDDLE  ALT=\"x+%2B+1+=+%283x+%2B+1%29+%2F+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply both sides of this equation by x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%2B1%29+=+3x+%2B+1 ALIGN=MIDDLE  ALT=\"x%28x%2B1%29+=+3x+%2B+1\"   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+%2B+x+=+3x+%2B+1 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+=+3x+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set equal to zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2x+-+1+=+0+ ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+-+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve by quadratic formula, where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-+sqrt+%28b%5E2+-+4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-+sqrt+%28b%5E2+-+4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a= 1, b= -2, c = -1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-2%29%2B-+sqrt+%28%28-2%29%5E2+-+4%2A%281%29%2A%28-1%29%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-2%29%2B-+sqrt+%28%28-2%29%5E2+-+4%2A%281%29%2A%28-1%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+=+%282%2B-+sqrt+%284+%2B+4%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%282%2B-+sqrt+%284+%2B+4%29%29%2F%282%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+=+%282+%2B-+sqrt+%288%29+%29%2F+2+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+sqrt+%288%29+%29%2F+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=x+=+%282+%2B-+2%2A+sqrt+%282%29%29+%2F+2+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B-+2%2A+sqrt+%282%29%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor the numerator, so you can reduce the fraction:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282%281+%2B-sqrt+%282%29%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%282%281+%2B-sqrt+%282%29%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+=1+%2B+sqrt+%282%29++ ALIGN=MIDDLE  ALT=\"x+=1+%2B+sqrt+%282%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+1+-+sqrt+%282%29 ALIGN=MIDDLE  ALT=\"x=+1+-+sqrt+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "However, the second solution is a negative number, which is NOT allowed in the last ln expression.  So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1+%2B+sqrt+%282%29 ALIGN=MIDDLE  ALT=\"x+=+1+%2B+sqrt+%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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