document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320816>Question 320816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: 5^x= (7)(3^x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229722 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=229722\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5^x\ =\ 7\,\cdot\,3^x\">\r<BR>\n" );
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document.write( "Take the natural log of both sides (actually, it can be the log to any base as it won't matter in the end).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(5^x\right)\ =\ \ln\left(7\,\cdot\,3^x\right)\">\r<BR>\n" );
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document.write( "The log of the product is the sum of the logs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(5^x\right)\ =\ \ln\left(7\right)\ +\ \ln\left(3^x\right)\">\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\ln\left(3^x\right)\"> to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ln\left(5^x\right)\ -\ \ln\left(3^x\right)\ =\ \ln\left(7\right)\">\r<BR>\n" );
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document.write( "Then use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)\">\r<BR>\n" );
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document.write( "so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ln\left(5\right)\ -\ x\ln\left(3\right)\ =\ \ln\left(7\right)\">\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\left(\ln\left(5\right)\ -\ \ln\left(3\right)\right)\ =\ \ln\left(7\right)\">\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\ln\left(\frac{5}{3}\right)\ =\ \ln\left(7\right)\">\r<BR>\n" );
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document.write( "Finally, multiply by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{\ln\left(\frac{5}{3}\right)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\ln\left(7\right)}{\ln\left(\frac{5}{3}\right)}\">\r<BR>\n" );
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document.write( "Use the calculator for a numerical approximation if necessary.\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" );
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