document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004909>Question 1004909</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log3(2x-3)-log3(x+2)=3\r<BR>\n" );
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document.write( "PLEASE HELP! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621263 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=621263\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Logarithm of a  quotient is the difference of the logarithms, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C2x-3%29-log%283%2Cx%2B2%29=red%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C2x-3%29-log%283%2Cx%2B2%29=red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-3%29%2F%28x%2B2%29%29=red%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-3%29%2F%28x%2B2%29%29=red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Logarithm of something is the exponent you have to apply the base to get that something, so if there is a solution,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-3%29%2F%28x%2B2%29%29=red%283%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-3%29%2F%28x%2B2%29%29=red%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B2%29=3%5Ered%283%29 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x%2B2%29=3%5Ered%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B2%29=27 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x%2B2%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The rest is simple algebra:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B2%29=27 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x%2B2%29=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29=27%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x-3%29=27%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3=27x%2B54 ALIGN=MIDDLE  ALT=\"2x-3=27x%2B54\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-27x=54%2B3 ALIGN=MIDDLE  ALT=\"2x-27x=54%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-25x=57 ALIGN=MIDDLE  ALT=\"-25x=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=57%2F%28-25%29 ALIGN=MIDDLE  ALT=\"x=57%2F%28-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-57%2F25=-%0D%0A2.28 ALIGN=MIDDLE  ALT=\"x=-57%2F25=-%0D%0A2.28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The problem is that with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2.28 ALIGN=MIDDLE  ALT=\"x=-2.28\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x-3=-7.56%2Cx%2B2=-0.28%29 ALIGN=MIDDLE  ALT=\"system%282x-3=-7.56%2Cx%2B2=-0.28%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and logarithm of a negative number is undefined.<BR>\n" );
document.write( "So, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28no%29 ALIGN=MIDDLE  ALT=\"highlight%28no%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28solutions%29 ALIGN=MIDDLE  ALT=\"highlight%28solutions%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We could have started with \"there are no solutions with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x-3%3C=0%2C%22or%22%2Cx%2B2%3C=0%29 ALIGN=MIDDLE  ALT=\"system%282x-3%3C=0%2C%22or%22%2Cx%2B2%3C=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%3C=3%2F2%2C%22or%22%2Cx%3C=-3%29 ALIGN=MIDDLE  ALT=\"system%28x%3C=3%2F2%2C%22or%22%2Cx%3C=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=3%2F2 ALIGN=MIDDLE  ALT=\"x%3C=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \".<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E3%2F2 ALIGN=MIDDLE  ALT=\"x%3E3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > both logarithms exist, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C2x-3%29-log%283%2Cx%2B2%29=log%283%2C%282x-3%29%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C2x-3%29-log%283%2Cx%2B2%29=log%283%2C%282x-3%29%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, if you were in calculus class (and even if you weren't),<BR>\n" );
document.write( "you would realize that in the domain of that function<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-3%29%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-3%29%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%282x-3%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-3%29%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-3%29%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-3%29%2F%28x%2B2%29=%282x%2B4-4%2B3%29%2F%28x%2B2%29=%282x%2B4%29%2F%28x%2B2%29-1%2F%28x%2B2%29=2-1%2F%28x%2B2%29%3C2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-3%29%2F%28x%2B2%29%29%3Clog%283%2C2%29%3C3 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-3%29%2F%28x%2B2%29%29%3Clog%283%2C2%29%3C3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Graphing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C%282x-3%29%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"log%283%2C%282x-3%29%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%283%2C2%29 ALIGN=MIDDLE  ALT=\"log%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C90%2C-5%2C5%2Clog%283%2C2x-3%29-log%283%2Cx%2B2%29%2Clog%283%2C2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );