document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187879>Question 187879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> log base 3 (x) = log base 3 (1/x)+4\r<BR>\n" );
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document.write( "i understand that log base 3 (1/x) is subtracted so the problem could look something like this log base 3 (x) -log base 3 (1/x)=4\r<BR>\n" );
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document.write( "have one question doesnt 1 and x become log base 3 (1)- log base 3 (x)\r<BR>\n" );
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document.write( "the answer is 9, -9 but i dont know how to set up the problem i am stuck </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140884 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=140884\">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 \ \ \ \ \ \ \ \ \ \ \log_3\, (x) = \log_3\,\left(\frac{1}{x}\right)+4\">\r<BR>\n" );
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document.write( "9 certainly could be (and is) the value of <i>x</i> that makes this equation a true statement, but -9 cannot be.  The domain of the <i>log</i> function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \{x\,|\,x\,\in\,\R,\ x > 0}\">\r<BR>\n" );
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document.write( "So if you were to say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\, (-9) = \log_3\,\left(\frac{1}{-9}\right)+4\">\r<BR>\n" );
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document.write( "What you would really be saying is: \"Some undefined thing is equal to some other undefined thing plus 4.\"  A patently absurd thing to say by any measure.\r<BR>\n" );
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document.write( "Having said all of that, here's how to do the problem correctly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\, (x) = \log_3\,\left(\frac{1}{x}\right)+4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\, (x) - \log_3\,\left(\frac{1}{x}\right)=4\">\r<BR>\n" );
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document.write( "Now, use \"The log of the quotient is the difference of the logs\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\, (x) - ( \log_3\,(1) - \log_3\,(x)) =4\">\r<BR>\n" );
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document.write( "Remove the parentheses and use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \log_b\,(1) = 0\"> to write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\, (x) + \log_3\,(x) =4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2 \log_3\,(x) =4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\,(x) =2\">\r<BR>\n" );
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document.write( "Since: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \log_b\,(x) = y \ \ \Rightarrow\ \ b^y = x\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \log_3\,(x) =2\ \ \Rightarrow\ \ 3^2 = x \ \ \Rightarrow\ \ x = 9\">\r<BR>\n" );
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document.write( "Where whomever gave you the answer of -9 may have gone wrong is they might have said:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2 \log_3\,(x) =4\ \ \Rightarrow\ \ \log_3\,(x^2)=4\ \ \Rightarrow\ \ 3^4 = x^2 \ \ \Rightarrow\ \ x^2 = 81\">\r<BR>\n" );
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document.write( "And the roots of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2 = 81\"> are 9 and -9, but you still have to go back to the original equation and consider any domain restrictions.  Therefore, you must exclude the negative root.\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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