document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128052>Question 128052</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x:<BR>\n" );
document.write( "logbase5(x+1)+logbase5(x-3)=1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93756 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C%28x%2B1%29%29%2Blog%285%2C%28x-3%29%29=1 ALIGN=MIDDLE  ALT=\"log%285%2C%28x%2B1%29%29%2Blog%285%2C%28x-3%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First thing is to use the rule that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Ca%29%2Blog%28b%2Cc%29=log%28b%2Cac%29 ALIGN=MIDDLE  ALT=\"log%28b%2Ca%29%2Blog%28b%2Cc%29=log%28b%2Cac%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%285%2C%28x%2B1%29%28x-3%29%29=1 ALIGN=MIDDLE  ALT=\"log%285%2C%28x%2B1%29%28x-3%29%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Next, we note that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Ca%29=y ALIGN=MIDDLE  ALT=\"log%28b%2Ca%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Ey=x ALIGN=MIDDLE  ALT=\"b%5Ey=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E1=%28x%2B1%29%28x-3%29 ALIGN=MIDDLE  ALT=\"5%5E1=%28x%2B1%29%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5=x%5E2-2x-3 ALIGN=MIDDLE  ALT=\"5=x%5E2-2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-8=0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28x-4%29%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<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;\" > or <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;\" >\r<BR>\n" );
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document.write( "However, <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;\" > means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3%3C0 ALIGN=MIDDLE  ALT=\"x-3%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28b%2Cx%29 ALIGN=MIDDLE  ALT=\"log%28b%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not defined for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C0 ALIGN=MIDDLE  ALT=\"x%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, therefore we need to exclude the second root.\r<BR>\n" );
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document.write( "The solution set consists of the single element 4. </SPAN>\n" );
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