document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148322>Question 148322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the value of x in logx + 1/logx = 5/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108713 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=108713\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the value of x in logx + 1/logx = 5/2\r<BR>\n" );
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document.write( "Multiply thru by 2logx to get:<BR>\n" );
document.write( "2(logx)^2 + 2 = 5logx<BR>\n" );
document.write( "Rearrange:<BR>\n" );
document.write( "2(logx)^2 - 5logx + 2 = 0<BR>\n" );
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document.write( "This is a quadratic with variable logx:<BR>\n" );
document.write( "Let logx = w and substitute:<BR>\n" );
document.write( "2w^2 -5w + 2 = 0<BR>\n" );
document.write( "Factor using the AC Method:<BR>\n" );
document.write( "2w^2-4w-w+2 = 0<BR>\n" );
document.write( "2w(w-2)-(w-2) = 0<BR>\n" );
document.write( "(w-2)(2w-1) = 0<BR>\n" );
document.write( "w = 2 or w = 1/2<BR>\n" );
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document.write( "Substiute back to logx:<BR>\n" );
document.write( "logx = 2 or logx = 1/2<BR>\n" );
document.write( "x = 10^2 or x = 10^(1/2)<BR>\n" );
document.write( "x = 100 or x = sqrt(10)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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