document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098778>Question 1098778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5^x=3-5^(2x)\r<BR>\n" );
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document.write( "Please help! Sorry I've been asking a lot of questions but I have a test tomorrow and we had a supply teacher who didn't know the material. The teacher left handouts without a lesson so I've been figuring things out on my own. More likely I'm really tired and can't concentrate. Sorry for the inconvenience.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713162 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13215)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>With the \"5^2x\" and \"5^x\" terms in the equation, this can be viewed as a \"quadratic\" equation in which the \"variable\" is 5^x, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%5Ex%29%5E2+=+5%5E%282x%29 ALIGN=MIDDLE  ALT=\"%285%5Ex%29%5E2+=+5%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So rewrite the equation as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E%282x%29+%2B+5%5Ex+-+3+=+0 ALIGN=MIDDLE  ALT=\"5%5E%282x%29+%2B+5%5Ex+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If it helps ease the confusion, you can define a new variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+5%5Ex ALIGN=MIDDLE  ALT=\"u+=+5%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > and write the equation as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+%2B+u+-+3+=+0 ALIGN=MIDDLE  ALT=\"u%5E2+%2B+u+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The quadratic does not factor, so use the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5Ex+=+%28-1%2B-sqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"5%5Ex+=+%28-1%2B-sqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since 5^x is never negative, we choose the positive solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5Ex+=+%28-1%2Bsqrt%2813%29%29%2F2 ALIGN=MIDDLE  ALT=\"5%5Ex+=+%28-1%2Bsqrt%2813%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then to solve for x, since it is an exponent, we take logs of both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Alog%285%29+=+log%28%28-1%2Bsqrt%2813%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"x%2Alog%285%29+=+log%28%28-1%2Bsqrt%2813%29%29%2F2%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+=+log%28%28-1%2Bsqrt%2813%29%29%2F2%29%2Flog%285%29 ALIGN=MIDDLE  ALT=\"x+=+log%28%28-1%2Bsqrt%2813%29%29%2F2%29%2Flog%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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