document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=553349>Question 553349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve algebraically 3e^x-6e^-x=4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360811 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=360811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Multiply both sides by e^x:<BR>\n" );
document.write( "3e^2x - 6 = 4 e^x\r<BR>\n" );
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document.write( "Set equal to zero, and place in descending power:\r<BR>\n" );
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document.write( "3e^2x - 4 e^x - 6 =0\r<BR>\n" );
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document.write( "Factor into the product of two binomials:  (3e^x-____)(e^x+_____)=0<BR>\n" );
document.write( "OOPS!! It doesn't factor, so you will have to use the quadratic formula to solve for e^x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3e%5E%282x%29+-+4e%5Ex+-+6+=+0 ALIGN=MIDDLE  ALT=\"3e%5E%282x%29+-+4e%5Ex+-+6+=+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=e%5Ex+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"e%5Ex+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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=e%5Ex=%284%2B-sqrt%2816-4%2A3%2A%28-6%29%29%29%2F%282%2A3%29+ ALIGN=MIDDLE  ALT=\"e%5Ex=%284%2B-sqrt%2816-4%2A3%2A%28-6%29%29%29%2F%282%2A3%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=e%5Ex+=+%284%2B-sqrt%2816%2B72%29%29%2F6 ALIGN=MIDDLE  ALT=\"e%5Ex+=+%284%2B-sqrt%2816%2B72%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex=+%284%2B-sqrt%2888%29%29%2F6 ALIGN=MIDDLE  ALT=\"e%5Ex=+%284%2B-sqrt%2888%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex=%284%2B-2sqrt%2822%29%29%2F6 ALIGN=MIDDLE  ALT=\"e%5Ex=%284%2B-2sqrt%2822%29%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Reduce the fraction by dividing by 2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+=+%282+%2B-+sqrt%2822%29%29%2F3 ALIGN=MIDDLE  ALT=\"e%5Ex+=+%282+%2B-+sqrt%2822%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the ln of each side:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5Ex%29+=+ln%28%282%2B-sqrt%2822%29%29%2F3%29+ ALIGN=MIDDLE  ALT=\"ln%28e%5Ex%29+=+ln%28%282%2B-sqrt%2822%29%29%2F3%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=x+=+ln%28%282%2B-sqrt%2822%29%29%2F3%29+ ALIGN=MIDDLE  ALT=\"x+=+ln%28%282%2B-sqrt%2822%29%29%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since you can't have an ln of a negative number, you can delete the solution involving the -sqrt(22) since it results in the ln of a negative.  The only answer that works is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+ln+%28%282+%2B+sqrt%2822%29%29%2F3%29+ ALIGN=MIDDLE  ALT=\"x+=+ln+%28%282+%2B+sqrt%2822%29%29%2F3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I wrote an entire curriculum for algebra, in particular for Logarithms, that might be helpful leading up to the skills in this problem!! You should see my \"College Algebra: One Step at a Time\". The easiest way to find this website is by use of the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the bottom of this page is a link that will take you to my FREE Homepage. Look near the top of this page for the link \"Basic, Intermediate, and College Algebra: One Step at a Time\", click on \"College Algebra\" and choose \"Chapter 4 Logarithms\".  I also have two 2-hour videos of me teaching logarithms in my younger years before I retired.  The videos can be found on my Homepage at the link \"Rapalje Videos in Living Color.\"  Everything on the website is FREE, even the videos!! \r<BR>\n" );
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document.write( "Happy New Year!! My Email address is rapaljer@seminolestate.edu if you need to contact me!! \r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida<BR>\n" );
document.write( "Altamonte Springs Campus \r<BR>\n" );
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