document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=685211>Question 685211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation 2^(2x) - 2^(x+1)-15=0       \r<BR>\n" );
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document.write( "Find the domain  f(x) = log((log((x-1)))) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424380 by </B><A HREF=/tutors/aboutme.mpl?userid=pmatei><B>pmatei(79)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=pmatei><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=424380\">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=2%5E%282x%29+-+2%5E%28x%2B1%29-15=0+++ ALIGN=MIDDLE  ALT=\"2%5E%282x%29+-+2%5E%28x%2B1%29-15=0+++\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Re-write it as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5Ex%29%5E2+-+2%2A2%5Ex+-+15+=+0 ALIGN=MIDDLE  ALT=\"%282%5Ex%29%5E2+-+2%2A2%5Ex+-+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+y ALIGN=MIDDLE  ALT=\"2%5Ex+=+y\"   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=y%5E2+-+2y+-+15+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+-+2y+-+15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve the quadratic in y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-5%29%28y%2B3%29=0 ALIGN=MIDDLE  ALT=\"%28y-5%29%28y%2B3%29=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=y+=+5 ALIGN=MIDDLE  ALT=\"y+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3 ALIGN=MIDDLE  ALT=\"y+=+-3\"   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=2%5Ex+=+-3 ALIGN=MIDDLE  ALT=\"2%5Ex+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > has no solution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5Ex+=+5 ALIGN=MIDDLE  ALT=\"2%5Ex+=+5\"   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%2Aln%282%29+=+ln%285%29 ALIGN=MIDDLE  ALT=\"x%2Aln%282%29+=+ln%285%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+=+%28ln%285%29%29%2F%28ln%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28ln%285%29%29%2F%28ln%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Domain for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=log%28%28log%28%28x-1%29%29%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=log%28%28log%28%28x-1%29%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The argument of logarithmic function has to be a positive number.\r<BR>\n" );
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document.write( "The first log has as argument log(x-1):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28%28x-1%29%29%3E0 ALIGN=MIDDLE  ALT=\"log%28%28x-1%29%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Logarithm function is positive if the argument is greater than 1. Logarithm of 1 is zero. And below 1 logarithm function is negative.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1%3E1 ALIGN=MIDDLE  ALT=\"x-1%3E1\"   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%3E2 ALIGN=MIDDLE  ALT=\"x%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the domain of f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E2 ALIGN=MIDDLE  ALT=\"x%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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