document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=434696>Question 434696</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the exponential equation.<BR>\n" );
document.write( "4^(x-1)=3^(2x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301061 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{x\,-\,1}\ =\ 3^{2x}\">\r<BR>\n" );
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document.write( "First note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3^{2x}\ =\ 9^x\"> so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{x\,-\,1}\ =\ 9^x\">\r<BR>\n" );
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document.write( "Take the log of both sides (any base, it doesn't matter)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(4^{x\,-\,1}\right)\ =\ \ln\left(9^x\right)\">\r<BR>\n" );
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document.write( "Use the laws of logs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \(x\ -\ 1)\ln\left(4\right)\ =\ x\ln\left(9\right)\">\r<BR>\n" );
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document.write( "Distribute and collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ln(4)\ -\ x\ln(9)\ =\ \ln(4)\">\r<BR>\n" );
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document.write( "Factor out the x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\left(\ln(4)\ -\ \ln(9)\right)\ =\ \ln(4)\">\r<BR>\n" );
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document.write( "The difference of the logs is the log of the quotient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\left(\ln\left(\frac{4}{9}\right)\right)\ =\ \ln(4)\">\r<BR>\n" );
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document.write( "Solve for x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\ln(4)}{\ln\left(\frac{4}{9}\right)}\">\r<BR>\n" );
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document.write( "Which is the exact simplifed answer, or you can use your calculator to get a numeric approximation to whatever precision is appropriate to your application.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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