document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=777872>Question 777872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If N=ab, show that 1/log (base a)N + 1/log (base b)N = 1\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #474324 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=474324\">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 \ \ \ \ \ \ \ \ \ \ \frac{1}{\log_a(ab)}\ +\ \frac{1}{\log_b(ab)}\ =^?\ 1\">\r<BR>\n" );
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document.write( "Use the base changing formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(ab)\ =\ \frac{\log_a(ab)}{\log_a(b)}\">\r<BR>\n" );
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document.write( "Then make the substitution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{\log_a(ab)}\ +\ \frac{\log_a(b)}{\log_a(ab)}\ =^?\ 1\">\r<BR>\n" );
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document.write( "But since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \log_\varphi(\varphi)\ =\ 1\">,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\log_a(a)}{\log_a(ab)}\ +\ \frac{\log_a(b)}{\log_a(ab)}\ =^?\ 1\">\r<BR>\n" );
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document.write( "Then, since the sum of the logs is the log of the product:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\log_a(ab)}{\log_a(ab)}\ =^?\ 1\">\r<BR>\n" );
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document.write( "Which is true for all a, b in the domain of the log function.\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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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