document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5155>Question 5155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving the following...<BR>\n" );
document.write( "ln(x)^(ln(x))=4\r<BR>\n" );
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document.write( "so far I took both sides times \"e\" to get...<BR>\n" );
document.write( "e^ln(x)^(ln(x))=e^4<BR>\n" );
document.write( "x^(ln(x))=e^4\r<BR>\n" );
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document.write( "but I don not know what to do next!!<BR>\n" );
document.write( "Thanks for the help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2631 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=2631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let me take a shot at this, since I found TWO solutions for it.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%28x%5E%28ln+x%29%29+=+4 ALIGN=MIDDLE  ALT=\"ln+%28x%5E%28ln+x%29%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the second law of logarithms, i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+%28M%5EN%29+=+N+%2A+log+M+ ALIGN=MIDDLE  ALT=\"log+%28M%5EN%29+=+N+%2A+log+M+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this can be written<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+%28x%5E%28ln+x%29%29+=+4 ALIGN=MIDDLE  ALT=\"ln+%28x%5E%28ln+x%29%29+=+4\"   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=%28ln+x%29+%2A+%28ln+x%29+=+4 ALIGN=MIDDLE  ALT=\"%28ln+x%29+%2A+%28ln+x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ln+x%29%5E2+=+4+ ALIGN=MIDDLE  ALT=\"%28ln+x%29%5E2+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the square root of each side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln+x+=++2+ ALIGN=MIDDLE  ALT=\"+ln+x+=++2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln+x+=+-2 ALIGN=MIDDLE  ALT=\"ln+x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In each case above, raise both sides as a power of e:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28ln+x%29+=+e%5E2 ALIGN=MIDDLE  ALT=\"e%5E%28ln+x%29+=+e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28ln+x%29+=+e%5E%28-2%29+ ALIGN=MIDDLE  ALT=\"e%5E%28ln+x%29+=+e%5E%28-2%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+=+e%5E2 ALIGN=MIDDLE  ALT=\"+x+=+e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+e%5E%28-2%29+ ALIGN=MIDDLE  ALT=\"x+=+e%5E%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The only question that remains is are these solutions both acceptable.  As far as I can tell, the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=e%5E%28-2%29+ ALIGN=MIDDLE  ALT=\"x=e%5E%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > never makes the ln of a negative, so BOTH answers should be included in the solution.\r<BR>\n" );
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document.write( "R^2 at SCC<BR>\n" );
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