document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5352>Question 5352</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x:\r<BR>\n" );
document.write( "\n" );
document.write( "ln(7-x)+ln(3x+5)=ln(24x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2790 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Combine logarithms on the left side using the law of logarithms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+a+%2B+ln+b+=+ln+%28ab%29+ ALIGN=MIDDLE  ALT=\"ln+a+%2B+ln+b+=+ln+%28ab%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ln(7-x)+ln(3x+5)=ln(24x)<BR>\n" );
document.write( "ln (7-x)(3x+5) = ln(24x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Raise both sides as a power of e to \"undo\" the lns:\r<BR>\n" );
document.write( "\n" );
document.write( "(7-x)(3x + 5) = 24x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x+%2B+35+-+3x%5E2+-+5x+-+24x+=+0 ALIGN=MIDDLE  ALT=\"21x+%2B+35+-+3x%5E2+-+5x+-+24x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8x+-+3x%5E2+%2B35+=+0 ALIGN=MIDDLE  ALT=\"-8x+-+3x%5E2+%2B35+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides by -1, and write in descending powers of x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+8x+-+35+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+8x+-+35+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which just happens to factor!! (Imagine that!!)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x-+7%29%28x%2B5%29+=+0+ ALIGN=MIDDLE  ALT=\"%283x-+7%29%28x%2B5%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+7%2F3 ALIGN=MIDDLE  ALT=\"x=+7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-5 ALIGN=MIDDLE  ALT=\"x=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You are not allowed to have a log of a negative in the real numbers, so you must reject the -5.  The final answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+7%2F3 ALIGN=MIDDLE  ALT=\"x=+7%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "R^2 at SCC<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );