document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53295>Question 53295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need to find the value of x here and i really need your help... i need the answer today at least before 6-9 in the morning... thanks...<BR>\n" );
document.write( "(4^(x-1))*(3^(x+2))=12^4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35531 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I answered this one using natural logs earlier today.  I hope you're not the same person and I just wasn't clear enough.  I will explain myself:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28x-1%29%2A3%5E%28x%2B2%29=12%5E4 ALIGN=MIDDLE  ALT=\"4%5E%28x-1%29%2A3%5E%28x%2B2%29=12%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the natural log of both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%284%5E%28x-1%29%2A3%5E%28x%2B2%29%29=ln%2812%5E4%29 ALIGN=MIDDLE  ALT=\"ln%284%5E%28x-1%29%2A3%5E%28x%2B2%29%29=ln%2812%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%28a%2Ab%29=ln%28a%29%2Bln%28b%29 ALIGN=MIDDLE  ALT=\"ln%28a%2Ab%29=ln%28a%29%2Bln%28b%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=ln%284%5E%28x-1%29%29%2Bln%283%5E%28x%2B2%29%29=ln%2812%5E4%29 ALIGN=MIDDLE  ALT=\"ln%284%5E%28x-1%29%29%2Bln%283%5E%28x%2B2%29%29=ln%2812%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%28a%5Eb%29=bln%28a%29 ALIGN=MIDDLE  ALT=\"ln%28a%5Eb%29=bln%28a%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=%28x-1%29ln%284%29%2B%28x%2B2%29ln%283%29=ln%2812%5E4%29 ALIGN=MIDDLE  ALT=\"%28x-1%29ln%284%29%2B%28x%2B2%29ln%283%29=ln%2812%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute ln(4) and ln(3).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xln%284%29-ln%284%29%2Bxln%283%29%2B2ln%283%29=ln%2812%5E4%29 ALIGN=MIDDLE  ALT=\"xln%284%29-ln%284%29%2Bxln%283%29%2B2ln%283%29=ln%2812%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add ln(4) and subtract 2ln(3) from both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xln%284%29-ln%284%29%2Bln%284%29%2Bxln%283%29%2B2ln%283%29-2ln%283%29=ln%2812%5E4%29%2Bln%284%29-2ln%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xln%284%29%2Bxln%283%29=ln%2812%5E4%29%2Bln%284%29-2ln%283%29 ALIGN=MIDDLE  ALT=\"xln%284%29%2Bxln%283%29=ln%2812%5E4%29%2Bln%284%29-2ln%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factor out x on the left side of the equation and use the fact that blna=lna^b to simplify the right side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28ln%284%29%2Bln%283%29%29=ln%2812%5E4%29%2Bln%284%29-ln%283%5E2%29 ALIGN=MIDDLE  ALT=\"x%28ln%284%29%2Bln%283%29%29=ln%2812%5E4%29%2Bln%284%29-ln%283%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the fact that lna+lnb=ln(a*b) and lna-lnb=ln(a/b)to simplify the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28ln%284%2A3%29%29=ln%28%2812%5E4%2A4%29%2F%283%5E2%29%29 ALIGN=MIDDLE  ALT=\"x%28ln%284%2A3%29%29=ln%28%2812%5E4%2A4%29%2F%283%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28ln%2812%29%29=ln%2820736%2A4%2F9%29 ALIGN=MIDDLE  ALT=\"x%28ln%2812%29%29=ln%2820736%2A4%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28ln%2812%29%29=ln%2882944%2F9%29 ALIGN=MIDDLE  ALT=\"x%28ln%2812%29%29=ln%2882944%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xln%2812%29=ln%289216%29 ALIGN=MIDDLE  ALT=\"xln%2812%29=ln%289216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by ln(12)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28xln%2812%29%29%2F%28ln%2812%29%29=%28ln%289216%29%29%2F%28ln%2812%29%29 ALIGN=MIDDLE  ALT=\"%28xln%2812%29%29%2F%28ln%2812%29%29=%28ln%289216%29%29%2F%28ln%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28ln%289216%29%29%2F%28ln%2812%29%29 ALIGN=MIDDLE  ALT=\"x=%28ln%289216%29%29%2F%28ln%2812%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Stick ln(9216) in your calculator=9.128696383.<BR>\n" );
document.write( "Stick ln(12) in your calculator=2.48490665.<BR>\n" );
document.write( "so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.128696383%2F2.48490665 ALIGN=MIDDLE  ALT=\"x=9.128696383%2F2.48490665\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.673657675 ALIGN=MIDDLE  ALT=\"x=3.673657675\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can verify this with a graphing calculator by finding the intersection between 4^(x-1)*3(x+2) and 12^4.<BR>\n" );
document.write( "If you plug your answer into the equation you get:<BR>\n" );
document.write( "20736.00006=20736 which is very close.  Keep in mind that we had to round off.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );