document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=137920>Question 137920</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question: - <BR>\n" );
document.write( "Log base 1/2(x-1)>0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100795 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=100795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Log base 1/2(x-1)>0<BR>\n" );
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document.write( "First: Note that x-1 must be > 0; i.e. x > 1<BR>\n" );
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document.write( "Find the boundary point for the inequality:<BR>\n" );
document.write( "log(1/2) (x-1) = 0<BR>\n" );
document.write( "x-1 = (1/2)^0<BR>\n" );
document.write( "x-1 = 1<BR>\n" );
document.write( "x = 2<BR>\n" );
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document.write( "Check a test point from the left interval and from the right interval.<BR>\n" );
document.write( "If x = 3, log(1/2) (2) > 0, this is false so no solutions in (2,+inf)<BR>\n" );
document.write( "If 1 < x < 2; pick x=3/2: log(1/2) (3/2-1) = 1 > 0 , so there are<BR>\n" );
document.write( "solutions in 1 < x < 2<BR>\n" );
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document.write( "Final Answer: 1 < x < 2<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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