document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=376752>Question 376752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write as a single log expression:<BR>\n" );
document.write( "2(log(x)+log(x^2+1))-3log(x-2)<BR>\n" );
document.write( "log(x^2)+log(x^4+1)-log(x^3-8)<BR>\n" );
document.write( "log(x^2(x^4+1)-log(x^3-8)<BR>\n" );
document.write( "log(x^6+x^2)-log(x^3-8)<BR>\n" );
document.write( "log(x^12)-log(x^3-8)<BR>\n" );
document.write( "log[(x^12)/(x^3-8)]<BR>\n" );
document.write( "??? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #268007 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=268007\">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( "The regular rules of algebra don't get suspended just because you are working with logarithms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\left(\log(x)\ +\ \log\left(x^2\ +\ 1\right)\right)\ -\ 3\log(x\ -\ 2)\">\r<BR>\n" );
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document.write( "First use\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_b(\chi) + \log_b(\upsilon)\ =\ \log_b(\chi\upsilon)\">\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 \ \ \ \ \ \ \ \ \ \ 2\left(\log\left(x^3\ +\ x\right)\right)\ -\ 3\log(x\ -\ 2)\">\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 \ \ \ \ \ \ \ \ \ \ n\log_b(\chi)\ =\ \log_b(\chi^n)\">\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 \ \ \ \ \ \ \ \ \ \ \log\left(\left(x^3\ +\ x\right)^2\right)\ -\ \log\left((x\ -\ 2)^3\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(\chi) - \log_b(\upsilon)\ =\ log_b\left(\frac{\chi}{\upsilon}\right)\">\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 \ \ \ \ \ \ \ \ \ \ \log\left(\frac{\left(x^3\ +\ x\right)^2}{(x\ -\ 2)^3}\right)\">\r<BR>\n" );
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document.write( "Which satisfies the requirements of the problem.  You could multiply out the two binomials, but that would be a decision  based on the requirements of further calculations.\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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