document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177517>Question 177517</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279069/algebrahomeworkh>Precalculus graphs and models</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> the problem is:<BR>\n" );
document.write( " log base of 2 times (x+20) minus log base of 2 times (x+2) is equal to log base of 2 x.\r<BR>\n" );
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document.write( "this is how far i have gotten:<BR>\n" );
document.write( "log base of 2 times (x+20/x+2) is equal to log base of 2 x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132538 by </B><A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><B>Electrified_Levi(103)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Electrified_Levi><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=132538\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, Hope I can help<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C%28x%2B20%29%29-+log+%282%2C%28x%2B2%29%29+=+log+%282%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log+%282%2C%28x%2B20%29%29-+log+%282%2C%28x%2B2%29%29+=+log+%282%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You are correct<BR>\n" );
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document.write( "If you subtract the same number log by the log, it is the same as one complete log as a fraction/division<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C%28%28x%2B20%29%2F%28x%2B2%29%29%29+=+log+%282%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log+%282%2C%28%28x%2B20%29%2F%28x%2B2%29%29%29+=+log+%282%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is where you got stuck, from here we can use a really easy method called \"undo\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C%28%28x%2B20%29%2F%28x%2B2%29%29%29+=+log+%282%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log+%282%2C%28%28x%2B20%29%2F%28x%2B2%29%29%29+=+log+%282%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since this equation has the same base/log (2) on both sides, we can just \"undo\" , get rid of, erase, cross out the logs<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C%28%28x%2B20%29%2F%28x%2B2%29%29%29+=+log+%282%2Cx%29+ ALIGN=MIDDLE  ALT=\"+log+%282%2C%28%28x%2B20%29%2F%28x%2B2%29%29%29+=+log+%282%2Cx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B20%29%2F%28x%2B2%29+=+x+ ALIGN=MIDDLE  ALT=\"+%28x%2B20%29%2F%28x%2B2%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now just solve for \"x\"<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B20%29%2F%28x%2B2%29+=+x+ ALIGN=MIDDLE  ALT=\"+%28x%2B20%29%2F%28x%2B2%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will multiply each side by (x+2) to get rid of the fraction<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B20%29%2F%28x%2B2%29+=+x+ ALIGN=MIDDLE  ALT=\"+%28x%2B20%29%2F%28x%2B2%29+=+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B2%29%28%28x%2B20%29%2F%28x%2B2%29%29+=+x%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"+%28x%2B2%29%28%28x%2B20%29%2F%28x%2B2%29%29+=+x%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28x%2B2%29%28%28x%2B20%29%2Fhighlight%28x%2B2%29%29+=+x%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"+highlight%28x%2B2%29%28%28x%2B20%29%2Fhighlight%28x%2B2%29%29+=+x%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+cross%28x%2B2%29%28%28x%2B20%29%2Fcross%28x%2B2%29%29+=+x%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"+cross%28x%2B2%29%28%28x%2B20%29%2Fcross%28x%2B2%29%29+=+x%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B20+=+x%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"+x%2B20+=+x%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will use distribution on the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B20+=+x%28x%2B2%29+ ALIGN=MIDDLE  ALT=\"+x%2B20+=+x%28x%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B20+=+highlight%28x%29%28highlight%28x%29%2B2%29+ ALIGN=MIDDLE  ALT=\"+x%2B20+=+highlight%28x%29%28highlight%28x%29%2B2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B20+=+highlight%28x%29%28x%2Bhighlight%282%29%29+ ALIGN=MIDDLE  ALT=\"+x%2B20+=+highlight%28x%29%28x%2Bhighlight%282%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+20+=+x%5E2+%2B+2x+ ALIGN=MIDDLE  ALT=\"+x+%2B+20+=+x%5E2+%2B+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will now move \"x + 20\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+20+=+x%5E2+%2B+2x+ ALIGN=MIDDLE  ALT=\"+x+%2B+20+=+x%5E2+%2B+2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+x+%2B+20+-+20=+x%5E2+%2B+2x+-+x+-+20+ ALIGN=MIDDLE  ALT=\"+x+-+x+%2B+20+-+20=+x%5E2+%2B+2x+-+x+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+x%5E2+%2B+x+-+20+ ALIGN=MIDDLE  ALT=\"+0+=+x%5E2+%2B+x+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+x%5E2+%2B+x+-+20+ ALIGN=MIDDLE  ALT=\"+0+=+x%5E2+%2B+x+-+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x+-+20++=+0 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x+-+20++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is a quadratic equation, we can solve this equation by factoring<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+x+-+20++=+0 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+x+-+20++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To find the factors, we have to have multiples of \"-20\", and the multiples have to add up to the middle term, or \"1\"<BR>\n" );
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document.write( "Factors of (-20)<BR>\n" );
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document.write( "(2,(-10)) No<BR>\n" );
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document.write( "(4,(-5)) No<BR>\n" );
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document.write( "(5,(-4)) Yes, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+%2B+%28-4%29+=+1+ ALIGN=MIDDLE  ALT=\"+5+%2B+%28-4%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these factors add up to \"1\")<BR>\n" );
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document.write( "Since there was only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that means there are only \"x's\"<BR>\n" );
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document.write( "(x)(x), you would then put the factors inside<BR>\n" );
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document.write( "(x+5)(x-4) are the factors, you can check using the foil method, but I already checked<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B5%29%28x-4%29+=+0+ ALIGN=MIDDLE  ALT=\"+%28x%2B5%29%28x-4%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now we can solve for \"x\", you can find \"x\" by putting each factor equal to zero<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+5+=+0+ ALIGN=MIDDLE  ALT=\"+x+%2B+5+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now move \"5\" to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+5+-+5+=+0+-+5+ ALIGN=MIDDLE  ALT=\"+x+%2B+5+-+5+=+0+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-5%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+4+=+0+ ALIGN=MIDDLE  ALT=\"+x+-+4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, now move (-4) to the right side<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+4+%2B+4+=+0+%2B+4+ ALIGN=MIDDLE  ALT=\"+x+-+4+%2B+4+=+0+%2B+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-5%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "These are your answers, but, you have to make sure and plug your answers into the original equation, and make sure that the numbers don't make a negative, because you can't take the log of a negative number<BR>\n" );
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document.write( "(-5), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C%28%28-5%29%2B20%29%29-+log+%282%2C%28%28-5%29%2B2%29%29+=+log+%282%2C%28-5%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, we don't have to go any further, since we already found a negative,  (-5) will not work<BR>\n" );
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document.write( "(4), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C%284%2B20%29%29-+log+%282%2C%284%2B2%29%29+=+log+%282%2C4%29+ ALIGN=MIDDLE  ALT=\"+log+%282%2C%284%2B20%29%29-+log+%282%2C%284%2B2%29%29+=+log+%282%2C4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%282%2C24%29-+log+%282%2C%286%29%29+=+log+%282%2C4%29+ ALIGN=MIDDLE  ALT=\"+log+%282%2C24%29-+log+%282%2C%286%29%29+=+log+%282%2C4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, there are no negatives, \"4\" will work<BR>\n" );
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document.write( "Here is the graph of the equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28500%2C500%2C-10%2C10%2C-10%2C10%2C+log+%28+2%2C+%28x%2B20%29%2F%28x%5E2%2B2x%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Remember though that you cannot take the log of a negative, your only answer is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+4+ ALIGN=MIDDLE  ALT=\"+x+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Hope I helped, Levi </SPAN>\n" );
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