document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106424>Question 1106424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can I please get help solving these equations to find the value of x and can I please see the working as I am unsure of how to solve them:\r<BR>\n" );
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document.write( "i)e^2x  +  5e^x  + 6 = 0<BR>\n" );
document.write( "ii) ln (x+4) + ln(x-2) = ln 7<BR>\n" );
document.write( "iii) 3 tan^3 (x)   - 3 tan^2 (x)  - tan (x) + 1 = 0\r<BR>\n" );
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document.write( "Thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721407 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29++%2B++5e%5Ex++%2B+6+=+0 ALIGN=MIDDLE  ALT=\"e%5E%282x%29++%2B++5e%5Ex++%2B+6+=+0\"   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 ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > squared is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29 ALIGN=MIDDLE  ALT=\"e%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this is a \"quadratic\" in which the \"variable\" is <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;\" >.  So factor it like a quadratic:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%2B3%29%28e%5Ex%2B2%29+=+0 ALIGN=MIDDLE  ALT=\"%28e%5Ex%2B3%29%28e%5Ex%2B2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and solve from there.<br><BR>\n" );
document.write( "However, you don't really need to do anything algebraically with this one if you think about it.  Both <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29 ALIGN=MIDDLE  ALT=\"e%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are always positive, so the left side of the equation is always positive; that of course means the solution set will be empty.<br><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%28x%2B4%29+%2B+ln%28x-2%29+=+ln+%287%29 ALIGN=MIDDLE  ALT=\"ln+%28x%2B4%29+%2B+ln%28x-2%29+=+ln+%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use your rules of logarithms.  The sum of logs is the log of the product:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28%28x%2B4%29%28x-2%29%29+=+ln%287%29 ALIGN=MIDDLE  ALT=\"ln%28%28x%2B4%29%28x-2%29%29+=+ln%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If the logs are equal, then the expressions are equal:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-2%29+=+7 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-2%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a quadratic which you can solve by any of a number of methods.<br><BR>\n" );
document.write( "(3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%28tan%28x%29%29%5E3+++-+3+%28tan%28x%29%29%5E2++-+tan%28x%29+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"3+%28tan%28x%29%29%5E3+++-+3+%28tan%28x%29%29%5E2++-+tan%28x%29+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The most common way of factoring an expression with four terms is by grouping.  Take the common factor out of the first two terms to give you an idea of what to do with the last two terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28tan%28x%29%29%5E2%2A%28tan%28x%29-1%29+-1%28tan%28x%29-1%29+=+0 ALIGN=MIDDLE  ALT=\"3%28tan%28x%29%29%5E2%2A%28tan%28x%29-1%29+-1%28tan%28x%29-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "There is now a common factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29-1 ALIGN=MIDDLE  ALT=\"tan%28x%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%28tan%28x%29%29%5E2-1%29%2A%28tan%28x%29-1%29+=+0 ALIGN=MIDDLE  ALT=\"%283%28tan%28x%29%29%5E2-1%29%2A%28tan%28x%29-1%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=3%28tan%28x%29%29%5E2-1+=+0 ALIGN=MIDDLE  ALT=\"3%28tan%28x%29%29%5E2-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29-1+=+0 ALIGN=MIDDLE  ALT=\"tan%28x%29-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And again finishing from there should be easy. </SPAN>\n" );
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