document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=378300>Question 378300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question1: log(x-2)+log(x+1)=2\r<BR>\n" );
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document.write( "This is what I have so far.. However, I'm not confident it's correct. Please help. Thank you!!\r<BR>\n" );
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document.write( "log[(x-2)(x+1)]=2<BR>\n" );
document.write( "b=1 p=2 x=(x-2)(x+1)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268823 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=268823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(x-2) + log(x+1) = 2<BR>\n" );
document.write( "You are correct with<BR>\n" );
document.write( "log((x-2)(x+1)) = 2<BR>\n" );
document.write( "But I am confused with the \"b=1 p=2 and x=(x-2)(x+1)\"<br><BR>\n" );
document.write( "The next step is to rewrite the equation in exponential form. In general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C+%28p%29%29+=+q ALIGN=MIDDLE  ALT=\"log%28a%2C+%28p%29%29+=+q\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+a%5Eq ALIGN=MIDDLE  ALT=\"p+=+a%5Eq\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Using this on our equation we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B1%29+=+10%5E2 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B1%29+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Since the base of log is 10.)<BR>\n" );
document.write( "Simplifying each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-x+-2+=+100 ALIGN=MIDDLE  ALT=\"x%5E2+-x+-2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a quadratic equation so we want one side to be zero. Subtracting 100 from each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-x+-+102+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-x+-+102+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This will not factor but we can use the Quadratic Formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-1%29+%2B-+sqrt%28%28-1%29%5E2+-+4%281%29%28-102%29%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-1%29+%2B-+sqrt%28%28-1%29%5E2+-+4%281%29%28-102%29%29%29%2F2%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-1%29+%2B-+sqrt%281+-+4%281%29%28-102%29%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-1%29+%2B-+sqrt%281+-+4%281%29%28-102%29%29%29%2F2%281%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+=+%28-%28-1%29+%2B-+sqrt%281+%2B+408%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-1%29+%2B-+sqrt%281+%2B+408%29%29%2F2%281%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+=+%28-%28-1%29+%2B-+sqrt%28409%29%29%2F2%281%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-1%29+%2B-+sqrt%28409%29%29%2F2%281%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+=+%281+%2B-+sqrt%28409%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+%2B-+sqrt%28409%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In long form this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+%2B+sqrt%28409%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+%2B+sqrt%28409%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+-+sqrt%28409%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+-+sqrt%28409%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When solving equations where the variable is in the argument (or base) of a logarithm, you must check you answers. You must make sure that all arguments (and bases) of logarithms are positive. If a \"solution\" makes an argument (or base) negative or zero then that \"solution\" must be rejected. This can happen <i>even if no mistakes were made while finding the solution!</i> This is why we must check out answers in problems like this.<br><BR>\n" );
document.write( "When checking answers use the original equation:<BR>\n" );
document.write( "log(x-2) + log(x+1) = 2<BR>\n" );
document.write( "Checking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+%2B+sqrt%28409%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+%2B+sqrt%28409%29%29%2F2\"   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%28%28%281+%2B+sqrt%28409%29%29%2F2%29+-+2%29%29+%2B+log%28%28%28%281+%2B+sqrt%28409%29%29%2F2%29%2B1%29%29+=+2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28409%29+%3E+20 ALIGN=MIDDLE  ALT=\"sqrt%28409%29+%3E+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > we should be able to see that both arguments will be positive. So there is no reason to reject this solution. The rest of the check is optional. It will determine if we made a mistake. I'll leave that up to you.<br><BR>\n" );
document.write( "Checking <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+-+sqrt%28409%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+-+sqrt%28409%29%29%2F2\"   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%28%28%281+-+sqrt%28409%29%29%2F2%29+-+2%29%29+%2B+log%28%28%28%281+-+sqrt%28409%29%29%2F2%29%2B1%29+=+2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28409%29+%3E+20 ALIGN=MIDDLE  ALT=\"sqrt%28409%29+%3E+20\"   DISABLED_style= \"max-width:90%; height:auto;\" > we should be able to see that both arguments will be negative! So we must reject this \"solution\".<br><BR>\n" );
document.write( "So the only solution to your equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281+%2B+sqrt%28409%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%281+%2B+sqrt%28409%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );