document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=581749>Question 581749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is:<BR>\n" );
document.write( "log(base x)2 + log(base2)x= -2\r<BR>\n" );
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document.write( "What I did:<BR>\n" );
document.write( "log(base x)2 + log(base2)x= -2<BR>\n" );
document.write( "log(base x)2+ 1/log(base x)2= -2<BR>\n" );
document.write( "(log (base x)2)^2 + 1= -2log(base x)2<BR>\n" );
document.write( "Take log(base x)2 as a:<BR>\n" );
document.write( "a^2 + 1= -2a<BR>\n" );
document.write( "a^2 + 2a + 1= 0<BR>\n" );
document.write( "(a+1)(a+1)=0<BR>\n" );
document.write( "a+1=0<BR>\n" );
document.write( "a=-1<BR>\n" );
document.write( "log(base x)2= -1<BR>\n" );
document.write( "x^-1= 2<BR>\n" );
document.write( "x= 1/2\r<BR>\n" );
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document.write( "I tried doing this, but I'm not sure if I'm right =)<BR>\n" );
document.write( "Thanks in advance!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371795 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=371795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log(base x)2 + log(base2)x= -2<BR>\n" );
document.write( "convert to base 10<BR>\n" );
document.write( "log2/logx+logx/log2=-2<BR>\n" );
document.write( "LCD:log2logx<BR>\n" );
document.write( "log2^2+logx^2=-2log2logx<BR>\n" );
document.write( "logx^2+2log2logx+log2^2=0<BR>\n" );
document.write( "let u=logx<BR>\n" );
document.write( "u^2=logx^2<BR>\n" );
document.write( "Using quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=1, b=2log2, c=log2^2<BR>\n" );
document.write( "u={-2log2±&#8730;[4log2^2-4*1*log2^2]}/2*1<BR>\n" );
document.write( "u=[-2log2±&#8730;(4log2^2-4log2^2)]/2<BR>\n" );
document.write( "u=[-2log2±&#8730;(0)]/2<BR>\n" );
document.write( "u=-2log2/2<BR>\n" );
document.write( "u=-log2=logx<BR>\n" );
document.write( "log(1/2)=log2^-1=-1*log2=-log2<BR>\n" );
document.write( "x=1/2<BR>\n" );
document.write( "I got the same answer so we may be doing it right. I had some difficulty following your computations, but your method is probably ok.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );