document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=615879>Question 615879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve 4^2t = 5^4t+4]\r<BR>\n" );
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document.write( "I get -2.5803 but i think I did something wrong.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #387370 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=387370\">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( "I have to presume you mean\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{2t}\ =\ 5^{4t\,+\,4}\">\r<BR>\n" );
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document.write( "Because the only way I know to solve\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{2t}\ =\ 5^{4t}\ +\ 4\">\r<BR>\n" );
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document.write( "Is to find an approximate root by numerical methods.\r<BR>\n" );
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document.write( "Be that as it may, your intuition is spot on.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{2(-2.5803)}\ \neq\ 5^{4(-2.5803)\,+\,4}\">\r<BR>\n" );
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document.write( "(order of magnitude difference)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 4^{2t}\ =\ 5^{4t\,+\,4}\">\r<BR>\n" );
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document.write( "Take the log of both sides (any base, 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^{2t}\right)\ =\ \ln\left(5^{4t\,+\,4}\right)\"> \r<BR>\n" );
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document.write( "Use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_b\left(a^n\right)\ =\ n\log_b(a)\">\r<BR>\n" );
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document.write( "to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (2t)\ln\left(4\right)\ =\ (4t\,+\,4)\ln\left(5\right)\">\r<BR>\n" );
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document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{2\ln4}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ (2t\,+\,2)\frac{\ln\left(5\right)}{\ln\left(4\right)\">\r<BR>\n" );
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document.write( "Just for neatness sake, let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE C_1\ =\ \frac{\ln\left(5\right)}{\ln\left(4\right)\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{2C_1}{1\ -\ 2C_1\">\r<BR>\n" );
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document.write( "The rest is just calculator (or better, spreadsheet) work.\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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