document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254819>Question 254819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I go about this question? \r<BR>\n" );
document.write( "\n" );
document.write( "Find the value of x for:\r<BR>\n" );
document.write( "\n" );
document.write( "log2(x2 + 4x + 3) – log 2(x2 + x) = 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187118 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2C%28b%2Fc%29%29+=+log%28a%2Cb%29+-+log%28a%2Cc%29 ALIGN=MIDDLE  ALT=\"log%28a%2C%28b%2Fc%29%29+=+log%28a%2Cb%29+-+log%28a%2Cc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the reverse is also true, i.e.:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2Cb%29+-+log%28a%2Cc%29+=+log%28a%2C%28b%2Fc%29%29 ALIGN=MIDDLE  ALT=\"log%28a%2Cb%29+-+log%28a%2Cc%29+=+log%28a%2C%28b%2Fc%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "applying this rule of logarithms makes your equation become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28x%5E2+%2B+4x+%2B+3%29%2F%28x%5E2+%2B+x%29%29+=+4 ALIGN=MIDDLE  ALT=\"log%282%2C%28x%5E2+%2B+4x+%2B+3%29%2F%28x%5E2+%2B+x%29%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+log%282%2Cx%29 ALIGN=MIDDLE  ALT=\"y+=+log%282%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ey+=+x ALIGN=MIDDLE  ALT=\"2%5Ey+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, applying this rule makes your equation become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4+=+%28x%5E2+%2B+4x+%2B+3%29%2F%28x%5E2+%2B+x%29 ALIGN=MIDDLE  ALT=\"2%5E4+=+%28x%5E2+%2B+4x+%2B+3%29%2F%28x%5E2+%2B+x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of this equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4+%2A+%28x%5E2+%2B+x%29=+%28x%5E2+%2B+4x+%2B+3%29 ALIGN=MIDDLE  ALT=\"2%5E4+%2A+%28x%5E2+%2B+x%29=+%28x%5E2+%2B+4x+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply the factors out and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Ax%5E2+%2B+16%2Ax+=+x%5E2+%2B+4%2Ax+%2B+3 ALIGN=MIDDLE  ALT=\"16%2Ax%5E2+%2B+16%2Ax+=+x%5E2+%2B+4%2Ax+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4%2Ax+%2B+3 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4%2Ax+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides of this equation and combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Ax%5E2+%2B+12%2Ax+-+3+=+0 ALIGN=MIDDLE  ALT=\"15%2Ax%5E2+%2B+12%2Ax+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "factor this equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Ax+-+3%29+%2A+%28x+%2B+1%29+=+0 ALIGN=MIDDLE  ALT=\"15%2Ax+-+3%29+%2A+%28x+%2B+1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F5%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "confirm by substituting in original equation of:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to confirm using your calculator, you need to convert the base of the logarithm from 2 to 10 or e.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I used 10 because it is the LOG function of my calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the conversion formula says:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28a%2Cb%29+=+log%28c%2Cb%29%2Flog%28c%2Ca%29 ALIGN=MIDDLE  ALT=\"log%28a%2Cb%29+=+log%28c%2Cb%29%2Flog%28c%2Ca%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if we let a = base of 2 and we let c = base of 10, this formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cb%29+=+log%2810%2Cb%29%2Flog%2810%2C2%29 ALIGN=MIDDLE  ALT=\"log%282%2Cb%29+=+log%2810%2Cb%29%2Flog%2810%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your formula of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2Cx%5E2+%2B+4x+%2B+3%29%2Flog%2810%2C2%29+-+log%2810%2Cx%5E2+%2B+x%29%2Flog%2810%2C2%29+=+4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substituting x = (1/5) into this equation, we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28.2%29%5E2+%2B+4%28.2%29+%2B+3%29%2Flog%2810%2C2%29+-+log%2810%2C%28.2%29%5E2+%2B+%28.2%29%29%2Flog%2810%2C2%29+=+4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.941106311+-+%28-2.058893689%29+=+4 ALIGN=MIDDLE  ALT=\"1.941106311+-+%28-2.058893689%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+4 ALIGN=MIDDLE  ALT=\"4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > confirming that x = (1/5) is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = -1, confirmation was not successful because:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "original equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4 ALIGN=MIDDLE  ALT=\"log%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute -1 for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C%28-1%29%5E2+%2B+%28-1%29%2Ax+%2B+3%29+-+log%282%2C%28-1%29%5E2+%2B+%28-1%29%29+=+4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%282%2C0%29+-+log%282%2C0%29+=+4 ALIGN=MIDDLE  ALT=\"log%282%2C0%29+-+log%282%2C0%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since you can't take log of 0 to any base, x = -1 is not a valid answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "graph of your original equation looks like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-4%2C2%2C-20%2C20%2Clog%282%2Cx%5E2+%2B+4x+%2B+3%29+-+log%282%2Cx%5E2+%2B+x%29+-+4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the answer to your problem is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F5%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );