document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92970>Question 92970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2(4^x+1) = 1\r<BR>\n" );
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document.write( "Solve for x.\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 #67660 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=67660\">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%284%5E%28x%2B1%29%29+=+1 ALIGN=MIDDLE  ALT=\"2%284%5E%28x%2B1%29%29+=+1\"   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%5E%28x%2B1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"4%5E%28x%2B1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F2%29%5E%28-2%29%29%5E%28x%2B1%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%28%281%2F2%29%5E%28-2%29%29%5E%28x%2B1%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 4 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E%28-2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%28-2%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=%281%2F2%29%5E%28-2%28x%2B1%29%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%28-2%28x%2B1%29%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E%28-2x-2%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%28-2x-2%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E%28-2x-2%29+=+%281%2F2%29%5E1 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E%28-2x-2%29+=+%281%2F2%29%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E1 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now that we have the same base, we can set the exponents equal to each other\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x=1%2B2 ALIGN=MIDDLE  ALT=\"-2x=1%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+x=3 ALIGN=MIDDLE  ALT=\"-2+x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms 2 and 1 on the right side to get 3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"x=%283%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide both sides by  -2 to isolate and solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-3+%2F+2 ALIGN=MIDDLE  ALT=\"x=+-3+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So our answer is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-3+%2F+2 ALIGN=MIDDLE  ALT=\"x=+-3+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "========================================================================\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%284%5E%28x%2B1%29%29+=+1 ALIGN=MIDDLE  ALT=\"2%284%5E%28x%2B1%29%29+=+1\"   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=2%284%5E%28%28-3%2F2%29%2B1%29%29+=+1 ALIGN=MIDDLE  ALT=\"2%284%5E%28%28-3%2F2%29%2B1%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3+%2F+2 ALIGN=MIDDLE  ALT=\"x=-3+%2F+2\"   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%284%5E%28-1%2F2%29%29+=+1 ALIGN=MIDDLE  ALT=\"2%284%5E%28-1%2F2%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28sqrt%284%5E-1%29%29+=+1 ALIGN=MIDDLE  ALT=\"2%28sqrt%284%5E-1%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E%28-1%2F2%29 ALIGN=MIDDLE  ALT=\"4%5E%28-1%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E-1%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E-1%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=2%28sqrt%281%2F4%29%29+=+1 ALIGN=MIDDLE  ALT=\"2%28sqrt%281%2F4%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E-1 ALIGN=MIDDLE  ALT=\"4%5E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   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%281%2F2%29+=+1 ALIGN=MIDDLE  ALT=\"2%281%2F2%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   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=1+=+1 ALIGN=MIDDLE  ALT=\"1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply. Since the two equations are equal, this verifies our answer.\r<BR>\n" );
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