document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=461820>Question 461820</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey,\r<BR>\n" );
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document.write( "Quick question. I have the following problem:\r<BR>\n" );
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document.write( "Using properties of logarithms, find the exact value of the expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%282%2C+25%29+log%283%2C+27%29+log%285%2C+8%29+ ALIGN=MIDDLE  ALT=\"+log%282%2C+25%29+log%283%2C+27%29+log%285%2C+8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I know Change-of-Base formula, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%28a%2C+M%29+=+%28log%28b%2C+M%29%29%2Flog%28b%2C+a%29 ALIGN=MIDDLE  ALT=\"+log+%28a%2C+M%29+=+%28log%28b%2C+M%29%29%2Flog%28b%2C+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log+%28a%2C+a%5Er%29=r ALIGN=MIDDLE  ALT=\"+log+%28a%2C+a%5Er%29=r\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but I don't know how to get to the answer, which is 18.\r<BR>\n" );
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document.write( "A little explanation of the steps would be much appreciated!\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jessica </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316641 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=316641\">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( "Ok, you are also going to need:\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( "Also note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 25\ =\ 5^2,\ \ \"> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 27\ =\ 3^3,\ \ \"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8\ =\ 2^3\">\r<BR>\n" );
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document.write( "The trick is to change all three of your log functions to the same base, but it doesn't matter which base.  I'm going to use natural logs, just because, well, it just seems natural.\r<BR>\n" );
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document.write( "Starting with\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_2(25)\ \cdot\ \log_3(27)\ \cdot\ \log_5(8)\">\r<BR>\n" );
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document.write( "Do the base conversion to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large e\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\ln(25)}{\ln(2)}\ \cdot\ \frac{\ln(27)}{\ln(3)}\ \cdot\ \frac{\ln(8)}{\ln(5)}\">\r<BR>\n" );
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document.write( "Make the substitutions alluded to earlier:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\ln(5^2)}{\ln(2)}\ \cdot\ \frac{\ln(3^3)}{\ln(3)}\ \cdot\ \frac{\ln(2^3)}{\ln(5)}\">\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( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{2\ln(5)}{\ln(2)}\ \cdot\ \frac{3\ln(3)}{\ln(3)}\ \cdot\ \frac{3\ln(2)}{\ln(5)}\">\r<BR>\n" );
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document.write( "Eliminating common factors leaves you with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\ \cdot\ 3\ \cdot\ 3\ =\ 18\">\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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