document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=486725>Question 486725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I need help in solving this logarith problem:-\r<BR>\n" );
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document.write( "Solve the simultaneous equations\r<BR>\n" );
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document.write( "log(x+y)= 2log(x)   (this equation doesn't have any base)<BR>\n" );
document.write( "log(y)= log(2)+ log(x-1)\r<BR>\n" );
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document.write( "My attempt:<BR>\n" );
document.write( "I simplified the first line :-\r<BR>\n" );
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document.write( "log(x+y)= 2log(x)<BR>\n" );
document.write( "=log(x,x+y)= log(x,x^2)  (I put the (x) as a base)<BR>\n" );
document.write( "=log(x,x+y)= 2  (I simplified log(x,x^2) to number 2)<BR>\n" );
document.write( "= x^2= x+y\r<BR>\n" );
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document.write( "Similarly I simplified the second line to be (y = 2x-2)\r<BR>\n" );
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document.write( "I don't know what to do any further now. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #332757 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=332757\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your work so far is good!<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+x%2By ALIGN=MIDDLE  ALT=\"x%5E2+=+x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-2 ALIGN=MIDDLE  ALT=\"y+=+2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute this for y in equaton 1) to get...<BR>\n" );
document.write( "1a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+x%2B%282x-2%29 ALIGN=MIDDLE  ALT=\"x%5E2+=+x%2B%282x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for x:<BR>\n" );
document.write( "1b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-3x%2B2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-3x%2B2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve by factoring:<BR>\n" );
document.write( "1c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x-2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so...<BR>\n" );
document.write( "1d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+1%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug each of these, in turn, in equation 2 and solve for y.<BR>\n" );
document.write( "2a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-2 ALIGN=MIDDLE  ALT=\"y+=+2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "2b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+0%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "2c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x-2 ALIGN=MIDDLE  ALT=\"y+=+2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "2d) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+=+2%29 ALIGN=MIDDLE  ALT=\"highlight%28y+=+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So there are four possible solutions:<BR>\n" );
document.write( "(1, 0), (1, 2), (2, 0), (2, 2)<BR>\n" );
document.write( "Let's check them all:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28x%2By%29+=+2Log%28x%29 ALIGN=MIDDLE  ALT=\"log%28x%2By%29+=+2Log%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Log%281%29+=+2Log%281%29 ALIGN=MIDDLE  ALT=\"Log%281%29+=+2Log%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=0+=+0 ALIGN=MIDDLE  ALT=\"0+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This solution is valid!<BR>\n" );
document.write( "Try the other solutions yourself and see what happens! </SPAN>\n" );
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