document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007427>Question 1007427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x. If 3^x=9x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623355 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> normally, when x is in the exponent, you would solve using logs.\r<BR>\n" );
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document.write( "you would take the log of both sides of the equation to get:\r<BR>\n" );
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document.write( "3^x = 9x becomes:\r<BR>\n" );
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document.write( "log(3^x) = log(9x) which becomes:\r<BR>\n" );
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document.write( "x * log(3) = log(9x)\r<BR>\n" );
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document.write( "solve for x and you get:\r<BR>\n" );
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document.write( "x = log(9x) / log(3)\r<BR>\n" );
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document.write( "it does not appear that there is a way to isolate x to one side of the equation.\r<BR>\n" );
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document.write( "if there is a way, i don't know it.\r<BR>\n" );
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document.write( "i usually solve these types of problems by graphing.\r<BR>\n" );
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document.write( "start with 3^x = 9x\r<BR>\n" );
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document.write( "subtract 9x from both sides of this eqaution to get 3^x - 9x = 0\r<BR>\n" );
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document.write( "you would graph y = 3^x - 9x and look for the zero crossing points.\r<BR>\n" );
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document.write( "those would be the common solutions.\r<BR>\n" );
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document.write( "doing it this way is the same as graphing y = 3^x and y = 9x and looking for the intersection points.\r<BR>\n" );
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document.write( "both methods would get you the same value of x.\r<BR>\n" );
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document.write( "the graph of y = 3^x - 9x is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/120202.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "you can see that the zero crossing points are at x = .128 and x = 3.\r<BR>\n" );
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document.write( "those are rounded values.\r<BR>\n" );
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document.write( "a graphing calculator such as the TI-86 plus will give you more decimal places in the result.\r<BR>\n" );
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document.write( "that calculator would tell you that the zero crossing points are at:\r<BR>\n" );
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document.write( "x = .12786942 and at x = 3\r<BR>\n" );
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document.write( "if you look at each equation individually, you will find that:\r<BR>\n" );
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document.write( "y = 3^x = 1.150824821 when x = .1278694246 and y = 9x = the same.\r<BR>\n" );
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document.write( "y = 3^x = 27 when x = 3 and y = 9x = the same.\r<BR>\n" );
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document.write( "i have yet to figure out how to do this algebraically, but if you have a good graphing calculator, you should always be able to find the solutuion graphically as long as the values are real.\r<BR>\n" );
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