document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130650>Question 130650</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%283x%2B1%29=1%2F%28e%5Ex-2%29 ALIGN=MIDDLE  ALT=\"e%5E%283x%2B1%29=1%2F%28e%5Ex-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95406 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=95406\">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=e%5E%283x%2B1%29=1%2F%28e%5E%28x-2%29%29 ALIGN=MIDDLE  ALT=\"e%5E%283x%2B1%29=1%2F%28e%5E%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%2Ae%5E%283x%29=1%2F%28e%5E%28x-2%29%29 ALIGN=MIDDLE  ALT=\"e%2Ae%5E%283x%29=1%2F%28e%5E%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%283x%2B1%29 ALIGN=MIDDLE  ALT=\"e%5E%283x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%283x%29%2Ae%5E1=e%2Ae%5E%283x%29 ALIGN=MIDDLE  ALT=\"e%5E%283x%29%2Ae%5E1=e%2Ae%5E%283x%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=e%2Ae%5E%283x%29=1%2F%28e%5Ex%2Fe%5E2%29 ALIGN=MIDDLE  ALT=\"e%2Ae%5E%283x%29=1%2F%28e%5Ex%2Fe%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28x-2%29 ALIGN=MIDDLE  ALT=\"e%5E%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28x%29%2Ae%5E%28-2%29=e%5Ex%2Fe%5E2 ALIGN=MIDDLE  ALT=\"e%5E%28x%29%2Ae%5E%28-2%29=e%5Ex%2Fe%5E2\"   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=e%2Ae%5E%283x%29=e%5E2%2Fe%5Ex ALIGN=MIDDLE  ALT=\"e%2Ae%5E%283x%29=e%5E2%2Fe%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Flip the fraction on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%28e%5Ex%29%5E3=e%5E2%2Fe%5Ex ALIGN=MIDDLE  ALT=\"e%28e%5Ex%29%5E3=e%5E2%2Fe%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%283x%29 ALIGN=MIDDLE  ALT=\"e%5E%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29%5E3 ALIGN=MIDDLE  ALT=\"%28e%5Ex%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=e%5Ex ALIGN=MIDDLE  ALT=\"u=e%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=e%2Au%5E3=e%5E2%2Fu ALIGN=MIDDLE  ALT=\"e%2Au%5E3=e%5E2%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=e%5Ex ALIGN=MIDDLE  ALT=\"u=e%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=e%2Au%5E3%2Au=e%5E2 ALIGN=MIDDLE  ALT=\"e%2Au%5E3%2Au=e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   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=e%2Au%5E4=e%5E2 ALIGN=MIDDLE  ALT=\"e%2Au%5E4=e%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E4=e%5E2%2Fe ALIGN=MIDDLE  ALT=\"u%5E4=e%5E2%2Fe\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   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=u%5E4=e ALIGN=MIDDLE  ALT=\"u%5E4=e\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29%5E4=e ALIGN=MIDDLE  ALT=\"%28e%5Ex%29%5E4=e\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=e%5Ex ALIGN=MIDDLE  ALT=\"u=e%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=e%5E%284x%29=e ALIGN=MIDDLE  ALT=\"e%5E%284x%29=e\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%284x%29=e%5E1 ALIGN=MIDDLE  ALT=\"e%5E%284x%29=e%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e ALIGN=MIDDLE  ALT=\"e\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E1 ALIGN=MIDDLE  ALT=\"e%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since the bases are equal, the exponents are equal\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=1 ALIGN=MIDDLE  ALT=\"4x=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=x=1%2F4 ALIGN=MIDDLE  ALT=\"x=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 to isolate x\r<BR>\n" );
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document.write( "Answer: \r<BR>\n" );
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document.write( "So our solution is \r<BR>\n" );
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