document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95610>Question 95610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> dear tutors i have been stumped with this question that did not come from a textbook, please try to answer it for me, thanks.<BR>\n" );
document.write( "log(2x) + log(x-1) - 2 log(x) = 1. you need to solve for x. i tried converting it into exponential form 10 = 2x(x-1)/x^2, = (2x^2-2x)/x^2 = (2x-2)/x and then multiplication of both sides by x to yield: 10x = 2x-2, then subtraction of 2x from both sides becomes: 8x = -2, division of both sides by 8 yields: x = -1/4 but it is impossible for x to have a negative value since it is impossible to perform a logarithm on a negative? thank you so much for taking the time to figure this out i really appreciate it </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69666 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(2x) + log(x-1) - 2 log(x) = 1<BR>\n" );
document.write( "Use the law that says loga + logb = logab<BR>\n" );
document.write( "and the law nloga = loga^n<BR>\n" );
document.write( "and the law loga - logb = log(a/b)<BR>\n" );
document.write( "to get:\r<BR>\n" );
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document.write( "-----------<BR>\n" );
document.write( "log[2x(x-1)]- logx^2 = 1\r<BR>\n" );
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document.write( "log [(2x^2-2x)/x^2] = 1\r<BR>\n" );
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document.write( "log [(2x-2)/x]= 1<BR>\n" );
document.write( "--------\r<BR>\n" );
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document.write( "Now change to exponential form to get:\r<BR>\n" );
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document.write( "[(2x-2)/x] = 10^1<BR>\n" );
document.write( "2x-2 = 10x<BR>\n" );
document.write( "x-1 = 5x<BR>\n" );
document.write( "4x = 1-<BR>\n" );
document.write( "x=-1/4\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "=================<BR>\n" );
document.write( "Check this answer in the original equation:\r<BR>\n" );
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document.write( "log(2x) + log(x-1) - 2 log(x) = 1<BR>\n" );
document.write( "x=-1/4 ?<BR>\n" );
document.write( "You get log(negative) + log(negative) - 2log(negative) = 1<BR>\n" );
document.write( "But there are no logs of negative values<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Conclusion: No solution\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );