document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1053172>Question 1053172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x, and write the EXACT answer using base-10 log.\r<BR>\n" );
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document.write( "(13^(-x+6))=(15^(-10x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #668400 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=668400\">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( "Note:  I follow the convention that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \log\"> means <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \log_{10}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 13^{-x\,+\,6}\ =\ 15^{-10x}\">\r<BR>\n" );
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document.write( "Take the log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log\left(13^{-x\,+\,6}\right)\ =\ \log\left(15^{-10x}\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(x^n\right)\ =\ n\log_b(x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (-x\,+\,6)\log\left(13\right)\ =\ (-10x)\log\left(15)\right)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{x\ -\ 6}{x}\ =\ \frac{10\log(15)}{\log(13)}\ =\ \frac{\log\left(15^{10}\right)}{\log(13)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ \frac{6}{x}\ =\ \frac{\log\left(15^{10}\right)}{\log(13)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{6}{x}\ =\ 1\ -\ \frac{\log\left(15^{10}\right)}{\log(13)}\ =\ \frac{\log(13)}{\log(13)}\ -\ \frac{\log\left(15^{10}\right)}{\log(13)}\ =\ \frac{\log(13)\ -\ \log\left(15^{10}\right)}{\log(13)}\">\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 \ \ \ \ \ \ \ \ \ \ \frac{6}{x}\ = \frac{\log\left(\frac{13}{15^{10}}\right)}{\log(13)}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{x}\ = \frac{\log\left(\frac{13}{15^{10}}\right)}{6\log(13)}\ =\ \frac{\log\left(\frac{13}{15^{10}}\right)}{\log(13^6)}\">\r<BR>\n" );
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document.write( "Take the reciprocal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{\log(13^6)}{\log\left(\frac{13}{15^{10}}\right)}\ =\ \frac{\log(4,826,809)}{\log\left(\frac{13}{576,650,390,625}\right)}\">\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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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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