document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=185080>Question 185080</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131808583/algebrahomeworkh>Prentice Hall Mathematics Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Having trouble with this question:\r<BR>\n" );
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document.write( "Solve for x. e is a number, not a variable<BR>\n" );
document.write( "2e^(x-2) = e^x + 7\r<BR>\n" );
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document.write( "So far, here is my work. I keep going in circles:<BR>\n" );
document.write( "e^(x-2) = (e^x + 7)/2<BR>\n" );
document.write( "ln(e^(x-2)) = ln((e^x + 7)/2)<BR>\n" );
document.write( "x-2 = ln(e^x + 7) - ln(2)<BR>\n" );
document.write( "I get lost here. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138865 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=138865\">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=2e%5E%28x-2%29+=+e%5Ex+%2B+7+ ALIGN=MIDDLE  ALT=\"2e%5E%28x-2%29+=+e%5Ex+%2B+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5E%28x%29%2Fe%5E2+=+e%5Ex+%2B+7 ALIGN=MIDDLE  ALT=\"2e%5E%28x%29%2Fe%5E2+=+e%5Ex+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28x-2%29 ALIGN=MIDDLE  ALT=\"e%5E%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28x%29%2Fe%5E2 ALIGN=MIDDLE  ALT=\"e%5E%28x%29%2Fe%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y-z%29=x%5Ey%2Fx%5Ez ALIGN=MIDDLE  ALT=\"x%5E%28y-z%29=x%5Ey%2Fx%5Ez\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   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=2e%5E%28x%29+=+e%5Ex%2Ae%5E2+%2B+7%2Ae%5E2 ALIGN=MIDDLE  ALT=\"2e%5E%28x%29+=+e%5Ex%2Ae%5E2+%2B+7%2Ae%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply EVERY term by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E2 ALIGN=MIDDLE  ALT=\"e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get rid of the fraction.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5E%28x%29+-+e%5Ex%2Ae%5E2+=+7%2Ae%5E2 ALIGN=MIDDLE  ALT=\"2e%5E%28x%29+-+e%5Ex%2Ae%5E2+=+7%2Ae%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex%2Ae%5E2 ALIGN=MIDDLE  ALT=\"e%5Ex%2Ae%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28x%29%282+-+e%5E2%29+=+7%2Ae%5E2 ALIGN=MIDDLE  ALT=\"e%5E%28x%29%282+-+e%5E2%29+=+7%2Ae%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   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%5E%28x%29+=+7%2Ae%5E2%2F%282+-+e%5E2%29 ALIGN=MIDDLE  ALT=\"e%5E%28x%29+=+7%2Ae%5E2%2F%282+-+e%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-+e%5E2 ALIGN=MIDDLE  ALT=\"2+-+e%5E2\"   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%5E%28x%29+=+-9.597 ALIGN=MIDDLE  ALT=\"e%5E%28x%29+=+-9.597\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the right side with a calculator. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+ln%28-9.597%29 ALIGN=MIDDLE  ALT=\"x+=+ln%28-9.597%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides (to eliminate the base \"e\")\r<BR>\n" );
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document.write( "Since you CANNOT take the natural log of a negative number (well at least for now...), this means that there is no solution. \r<BR>\n" );
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document.write( "So there are no solutions. I would double check the original problem.\r<BR>\n" );
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document.write( "As visual confirmation, graph the two expressions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2e%5E%28x-2%29 ALIGN=MIDDLE  ALT=\"2e%5E%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex+%2B+7 ALIGN=MIDDLE  ALT=\"e%5Ex+%2B+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you'll find that they do NOT cross. \r<BR>\n" );
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document.write( "Note: taking the log of a negative number will give you a complex number, but that's extra information...\r<BR>\n" );
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document.write( " </SPAN>\n" );
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