document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=913163>Question 913163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve: 16^(x) + 4^(x+1) - 3 = 0 \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #554330 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=554330\">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=16%5E%28x%29+%2B+4%5E%28x%2B1%29+-+3+=+0 ALIGN=MIDDLE  ALT=\"16%5E%28x%29+%2B+4%5E%28x%2B1%29+-+3+=+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=%284%5Ex%29%5E2+%2B+%284%5Ex%29%2A%284%29+-+3+=+0 ALIGN=MIDDLE  ALT=\"%284%5Ex%29%5E2+%2B+%284%5Ex%29%2A%284%29+-+3+=+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=z%5E2+%2B4z+-+3+=+0 ALIGN=MIDDLE  ALT=\"z%5E2+%2B4z+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+4%5Ex ALIGN=MIDDLE  ALT=\"z+=+4%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-2%2Bsqrt%287%29 ALIGN=MIDDLE  ALT=\"z+=+-2%2Bsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-2-sqrt%287%29 ALIGN=MIDDLE  ALT=\"z+=+-2-sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The steps for the quadratic formula are lengthy and I feel they would clutter up this solution page. Let me know if you need to see the steps to getting those solutions for z.\r<BR>\n" );
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document.write( "The solutions in terms of z are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-2%2Bsqrt%287%29 ALIGN=MIDDLE  ALT=\"z+=+-2%2Bsqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-2-sqrt%287%29 ALIGN=MIDDLE  ALT=\"z+=+-2-sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We ultimately want solutions in terms of x.\r<BR>\n" );
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document.write( "Plug in the first solution for z to get the first solution for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5Ex+=+-2%2Bsqrt%287%29 ALIGN=MIDDLE  ALT=\"4%5Ex+=+-2%2Bsqrt%287%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+=+log%284%2C%28-2%2Bsqrt%287%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+log%284%2C%28-2%2Bsqrt%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the first solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+log%284%2C%28-2%2Bsqrt%287%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+log%284%2C%28-2%2Bsqrt%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using a calculator, we get log(-2+sqrt(7))/log(4) = -0.3154747\r<BR>\n" );
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document.write( "Plug in the second solution for z to get the second solution for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-sqrt%287%29+=+4%5Ex ALIGN=MIDDLE  ALT=\"-2-sqrt%287%29+=+4%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=4%5Ex+=+-2-sqrt%287%29 ALIGN=MIDDLE  ALT=\"4%5Ex+=+-2-sqrt%287%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+=+log%284%2C%28-2-sqrt%287%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+log%284%2C%28-2-sqrt%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the second solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+log%284%2C%28-2-sqrt%287%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+log%284%2C%28-2-sqrt%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >; however, notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-sqrt%287%29=-4.64575 ALIGN=MIDDLE  ALT=\"-2-sqrt%287%29=-4.64575\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative. That means the log of this value is undefined. So log(-2-sqrt(7)) = log(-4.64575) = Undefined\r<BR>\n" );
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document.write( "Final Answer: \r<BR>\n" );
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document.write( "The only exact solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+log%284%2C%28-2%2Bsqrt%287%29%29%29 ALIGN=MIDDLE  ALT=\"x+=+log%284%2C%28-2%2Bsqrt%287%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The only approximate solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-0.3154747 ALIGN=MIDDLE  ALT=\"x+=+-0.3154747\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim \r<BR>\n" );
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