document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771697>Question 771697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I hope someone can clarify this. I'M CONFUSED!!!\r<BR>\n" );
document.write( "\n" );
document.write( "2(log4 x + logx 4)=5\r<BR>\n" );
document.write( "\n" );
document.write( "My working:<BR>\n" );
document.write( "2(log4 x + logx 4)=5<BR>\n" );
document.write( "(log4 x + logx 4)=5/2<BR>\n" );
document.write( "log4 x + (1/log4 x)=5/2\r<BR>\n" );
document.write( "\n" );
document.write( "Here is where my confusion is. I have 2 different workings.<BR>\n" );
document.write( "#1.<BR>\n" );
document.write( "log4 x + (1/log4 x)=5/2<BR>\n" );
document.write( "Let log4 x = m<BR>\n" );
document.write( "Thus, <BR>\n" );
document.write( "m + 1/m = 5/2<BR>\n" );
document.write( "[[(m^2)+1]/m]=5/2<BR>\n" );
document.write( "(2m^2)+2=5m<BR>\n" );
document.write( "(m-2)(2m-1)=0<BR>\n" );
document.write( "m=2 or 1/2\r<BR>\n" );
document.write( "\n" );
document.write( "when m=2,<BR>\n" );
document.write( "log4 x = m<BR>\n" );
document.write( "log4 x = 2<BR>\n" );
document.write( "x = 64\r<BR>\n" );
document.write( "\n" );
document.write( "when m=1/2,<BR>\n" );
document.write( "log4 x = m<BR>\n" );
document.write( "x=2\r<BR>\n" );
document.write( "\n" );
document.write( "#2.<BR>\n" );
document.write( "log4 x + (1/log4 x)=5/2<BR>\n" );
document.write( "[(log4 x)^2 + (1)/log4 x]=5/2<BR>\n" );
document.write( "[2(log4 x) + (1)/log4 x]=5/2<BR>\n" );
document.write( "Let log4 x = m<BR>\n" );
document.write( "Thus, (2m + 1)/m=5/2<BR>\n" );
document.write( "4m + 2 =5m<BR>\n" );
document.write( "m= 2\r<BR>\n" );
document.write( "\n" );
document.write( "when m=2,<BR>\n" );
document.write( "log4 x = m<BR>\n" );
document.write( "log4 x = 2<BR>\n" );
document.write( "x = 64\r<BR>\n" );
document.write( "\n" );
document.write( "I rechecked again, the correct answer should be m=1/2 and thus x=2. Can anyone tell me where did i do wrong for #2 working? And can anyone guide me how to determine the correct answer for #1 working? Please help me. Your help is much appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470374 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470374\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I hope someone can clarify this. I'M CONFUSED!!! <BR>\n" );
document.write( "2(log4 x + logx 4)=5 <BR>\n" );
document.write( "My working:<BR>\n" );
document.write( "2(log4 x + logx 4)=5<BR>\n" );
document.write( "(log4 x + logx 4)=5/2<BR>\n" );
document.write( "log4 x + (1/log4 x)=5/2 <BR>\n" );
document.write( "Here is where my confusion is. I have 2 different workings.<BR>\n" );
document.write( "#1.<BR>\n" );
document.write( "log4 x + (1/log4 x)=5/2<BR>\n" );
document.write( "Let log4 x = m<BR>\n" );
document.write( "Thus, <BR>\n" );
document.write( "m + 1/m = 5/2<BR>\n" );
document.write( "[[(m^2)+1]/m]=5/2<BR>\n" );
document.write( "(2m^2)+2=5m<BR>\n" );
document.write( "(m-2)(2m-1)=0<BR>\n" );
document.write( "m=2 or 1/2 <BR>\n" );
document.write( "when m=2,<BR>\n" );
document.write( "log4 x = m<BR>\n" );
document.write( "log4 x = 2<BR>\n" );
document.write( "x = 64 <BR>\n" );
document.write( "when m=1/2,<BR>\n" );
document.write( "log4 x = m<BR>\n" );
document.write( "x=2<BR>\n" );
document.write( "===========================================================<BR>\n" );
document.write( "#2.<BR>\n" );
document.write( "log4 x + (1/log4 x)=5/2<BR>\n" );
document.write( "[(log4 x)^2 + (1)/log4 x]=5/2  **** You squared the 1st term for no reason.<BR>\n" );
document.write( "====================================<BR>\n" );
document.write( "[2(log4 x) + (1)/log4 x]=5/2<BR>\n" );
document.write( "Let log4 x = m<BR>\n" );
document.write( "Thus, (2m + 1)/m=5/2<BR>\n" );
document.write( "4m + 2 =5m<BR>\n" );
document.write( "m= 2 <BR>\n" );
document.write( "when m=2,<BR>\n" );
document.write( "log4 x = m<BR>\n" );
document.write( "log4 x = 2<BR>\n" );
document.write( "x = 64 <BR>\n" );
document.write( "I rechecked again, the correct answer should be m=1/2 and thus x=2. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );