document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=884647>Question 884647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "I was wondering if anybody could help me solve this equation. I really don't quite understand it. I looked into my algebra 2 book online and I still didn't really grasp the concept, so can someone please help me. Thank you in advance. <BR>\n" );
document.write( "The equation is 1n(x+6)-1n(x)=!n(4). Give an exact solution.    </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534533 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general rule to follow is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28a%29+-+ln%28b%29+=+ln%28+a%2Fb+%29+ ALIGN=MIDDLE  ALT=\"+ln%28a%29+-+ln%28b%29+=+ln%28+a%2Fb+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "To attempt to show why this is so, <BR>\n" );
document.write( "suppose <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+e%2Ae%2Ae%2Ae%2Ae%2Ae+ ALIGN=MIDDLE  ALT=\"+a+=+e%2Ae%2Ae%2Ae%2Ae%2Ae+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( e = 2.2718 ), or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+e%5E5+ ALIGN=MIDDLE  ALT=\"+a+=+e%5E5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Also, suppose<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+e%2Ae%2Ae%2Ae+ ALIGN=MIDDLE  ALT=\"+b+=+e%2Ae%2Ae%2Ae+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+e%5E4+ ALIGN=MIDDLE  ALT=\"+b+=+e%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "So, now I can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28a%29+-+ln%28b%29+=+ln%28e%5E5%29+-+ln%28e%5E4%29+ ALIGN=MIDDLE  ALT=\"+ln%28a%29+-+ln%28b%29+=+ln%28e%5E5%29+-+ln%28e%5E4%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=+ln%28e%5E5%29+-+ln%28e%5E4%29+=+5+-+4+ ALIGN=MIDDLE  ALT=\"+ln%28e%5E5%29+-+ln%28e%5E4%29+=+5+-+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28e%5E5%29+-+ln%28e%5E4%29+=+1+ ALIGN=MIDDLE  ALT=\"+ln%28e%5E5%29+-+ln%28e%5E4%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "If you don't understand this last line, then<BR>\n" );
document.write( "you don't really know what a log is ( natural or not ) <BR>\n" );
document.write( "and you need intensive review<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Now, to prove my definition:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+a%2Fb+%29+=+ln%28+e%5E5+%2F+e%5E4+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+a%2Fb+%29+=+ln%28+e%5E5+%2F+e%5E4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+a%2Fb+%29+=+ln%28+e%5E1+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+a%2Fb+%29+=+ln%28+e%5E1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+a%2Fb+%29+=+1+ ALIGN=MIDDLE  ALT=\"+ln%28+a%2Fb+%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The definition works no matter what you<BR>\n" );
document.write( "plug in for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+ ALIGN=MIDDLE  ALT=\"+b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. I just made it easy.<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Now looking at your problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+x%2B6+%29+-+ln%28+x+%29+=+ln%284%29+ ALIGN=MIDDLE  ALT=\"+ln%28+x%2B6+%29+-+ln%28+x+%29+=+ln%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+%28x%2B6%29%2Fx+%29+=+ln%28+4+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+%28x%2B6%29%2Fx+%29+=+ln%28+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Is it clear that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x%2B6+%29%2Fx+=+4+ ALIGN=MIDDLE  ALT=\"+%28+x%2B6+%29%2Fx+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "The basic definition would be:<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28a%29+=+ln%28b%29+ ALIGN=MIDDLE  ALT=\"+ln%28a%29+=+ln%28b%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+b+ ALIGN=MIDDLE  ALT=\"+a+=+b+\"   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=+%28+x%2B6+%29%2Fx+=+4+ ALIGN=MIDDLE  ALT=\"+%28+x%2B6+%29%2Fx+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+6+=+4x+ ALIGN=MIDDLE  ALT=\"+x+%2B+6+=+4x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+=+6+ ALIGN=MIDDLE  ALT=\"+3x+=+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "----------<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+x%2B6+%29+-+ln%28+x+%29+=+ln%284%29+ ALIGN=MIDDLE  ALT=\"+ln%28+x%2B6+%29+-+ln%28+x+%29+=+ln%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+2%2B6+%29+-+ln%28+2+%29+=+ln%284%29+ ALIGN=MIDDLE  ALT=\"+ln%28+2%2B6+%29+-+ln%28+2+%29+=+ln%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+8+%29+-+ln%28+2+%29+=+ln%28+4+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+8+%29+-+ln%28+2+%29+=+ln%28+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+8%2F2+%29+=+ln%28+4+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+8%2F2+%29+=+ln%28+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+4+%29+=+ln%28+4+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+4+%29+=+ln%28+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "Hope this helps\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );