document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=22964>Question 22964</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP =) !\r<BR>\n" );
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document.write( "resolving the Question 2570 (p200 - 250) : log of 9 to the base square root of x - log of 3 to the base x = 9 + 6 log of x to the base square root of 3<BR>\n" );
document.write( "a tutor found x = 3^(1/4) or x = 1/3<BR>\n" );
document.write( "I only found one answer x = 3^(1/4) \r<BR>\n" );
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document.write( "Who is right ? And where is the (my?) flaw ?<BR>\n" );
document.write( "Thanks a lot !!!\r<BR>\n" );
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document.write( "Here is my answer :\r<BR>\n" );
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document.write( "logV\"\"x(9) - logx(3) = 9 + 6logV\"\"3(x)                       <BR>\n" );
document.write( "(logx 9) / (logx V\"\"x) - logx 3 = 9 + 6( (logx x) / (logx V\"\"3) )       <BR>\n" );
document.write( "(logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6( 1 / ( (logx 3) / 2 ) )   <BR>\n" );
document.write( "(logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6 / ( (logx 3) / 2 ) <BR>\n" );
document.write( "2logx 9 - logx 3 = 9 + 6 ( 2 / logx 3 )       <BR>\n" );
document.write( "2logx 9 - logx 3 = 9 + 12 / logx 3             <BR>\n" );
document.write( "logx 3 ( 2logx 9 - logx 3 - 9 ) = 12  <BR>\n" );
document.write( "logx 3 ( 4logx 3 - logx 3 - 9 ) = 12  <BR>\n" );
document.write( "logx 3 ( 3logx 3 - 9 ) = 12   <BR>\n" );
document.write( "3(logx 3)^2 - 9logx 3 = 12     <BR>\n" );
document.write( "(logx 3)^2 - 3logx 3 = 4<BR>\n" );
document.write( "logx 3 - 3 = 4 / (logx 3)<BR>\n" );
document.write( "logx 3 - 3 = 1/4 logx 3<BR>\n" );
document.write( "logx 3 - 3 = logx 3^(1/4)<BR>\n" );
document.write( "logx 3 - logx 3^(1/4) = 3<BR>\n" );
document.write( "logx (3/3^(1/4) ) = 3<BR>\n" );
document.write( "x^3 = 3/3^(1/4)                              <BR>\n" );
document.write( "x^3 = 3^(3/4)                  <BR>\n" );
document.write( "x^3 = 3^( (1/4) * 3 )<BR>\n" );
document.write( "x^3 = ( 3^(1/4) )^3<BR>\n" );
document.write( "x = 3^(1/4)   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #11341 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=11341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SEE MY COMMENTS BELOW\r<BR>\n" );
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document.write( "resolving the Question 2570 (p200 - 250) : log of 9 to the base square root of x - log of 3 to the base x = 9 + 6 log of x to the base square root of 3<BR>\n" );
document.write( "a tutor found x = 3^(1/4) or x = 1/3<BR>\n" );
document.write( "I only found one answer x = 3^(1/4) <BR>\n" );
document.write( "Who is right ? And where is the (my?) flaw ?<BR>\n" );
document.write( "Thanks a lot !!! <BR>\n" );
document.write( "Here is my answer : <BR>\n" );
document.write( "logV\"\"x(9) - logx(3) = 9 + 6logV\"\"3(x) OK.I SHALL USE YOUR NOTATION TO SHOW SQUAREROOT<BR>\n" );
document.write( "(logx 9) / (logx V\"\"x) - logx 3 = 9 + 6( (logx x) / (logx V\"\"3) )...GOOD.YOU TOOK EVERY LOG TO BASE X <BR>\n" );
document.write( "(logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6( 1 / ( (logx 3) / 2 ) )....VERY GOOD <BR>\n" );
document.write( "(logx 9) / ( (logx x) / 2 ) - logx 3 = 9 + 6 / ( (logx 3) / 2 )..VERY GOOD <BR>\n" );
document.write( "2logx 9 - logx 3 = 9 + 6 ( 2 / logx 3 ) .....VERY GOOD<BR>\n" );
document.write( "2logx 9 - logx 3 = 9 + 12 / logx 3 .......VERY GOOD<BR>\n" );
document.write( "logx 3 ( 2logx 9 - logx 3 - 9 ) = 12 ......VERY GOOD<BR>\n" );
document.write( "logx 3 ( 4logx 3 - logx 3 - 9 ) = 12 <BR>\n" );
document.write( "logx 3 ( 3logx 3 - 9 ) = 12 EXCELLENT<BR>\n" );
document.write( "3(logx 3)^2 - 9logx 3 = 12 ....CORRECT<BR>\n" );
document.write( "(logx 3)^2 - 3logx 3 = 4.........CORRECT...YOU HAVE DONE EXCEPTIONALLY WELL UP TO THIS .NOW BEST WAY O PROCEED IS..... FOR YOUR EASE OF UNDERSTANDING PUT<BR>\n" );
document.write( "LOGX 3 = Y..THEN WE HAVE...Y^2-3Y-4=0=Y^2-4Y+Y-4=0<BR>\n" );
document.write( "Y(Y-4)+1(Y-4)=0<BR>\n" );
document.write( "(Y-4)(Y+1)=0..<BR>\n" );
document.write( "Y=4 OR =-1<BR>\n" );
document.write( "LOGX 3=4..........................OR............... LOGX 3=-1<BR>\n" );
document.write( "X^4=3........................OR.........X^-1=3<BR>\n" );
document.write( "X=3^(1/4).....................OR..........X=3^-1=1/3<BR>\n" );
document.write( "NOW LET US SEE THE MISTAKE YOU DID<BR>\n" );
document.write( "logx 3 - 3 = 4 / (logx 3)...OK<BR>\n" );
document.write( "logx 3 - 3 = 1/4 logx 3.....HOW?THIS IS THE MISTAKE...OK...<BR>\n" );
document.write( "logx 3 - 3 = logx 3^(1/4)<BR>\n" );
document.write( "logx 3 - logx 3^(1/4) = 3<BR>\n" );
document.write( "logx (3/3^(1/4) ) = 3<BR>\n" );
document.write( "x^3 = 3/3^(1/4) <BR>\n" );
document.write( "x^3 = 3^(3/4) <BR>\n" );
document.write( "x^3 = 3^( (1/4) * 3 )<BR>\n" );
document.write( "x^3 = ( 3^(1/4) )^3<BR>\n" );
document.write( "x = 3^(1/4) <BR>\n" );
document.write( " I AM VERY HAPPY AT YOUR SINCERE ATTEMPT AND CORRECT ANALYSISALMOST TILL THE END.YOU WILL SURELY GO UP WITH THIS APPROACH.NOW LET ME GIVE YOU A TIP TO DO THIS EASIER..WHILE USING THE FORMULA <BR>\n" );
document.write( "TAKE LOGX Y=LOG Y/LOG X DROPPING THE BASE WHICH COULD BE ANY COMMON STANDARD BASE..SO THE INITIAL PROBLEM BECOMES<BR>\n" );
document.write( "log of 9 to the base square root of x - log of 3 to the base x = 9 + 6 log of x to the base square root of 3<BR>\n" );
document.write( "LOG 9/LOG SQRTX-LOG 3/LOG X=9+6*(LOG X/LOG SQRT3)..AND PROCEED ..THIS WILL SIMPLIFY THE WOKING AS YOU ARE NOT TO WORRY ABOUT THE BASE.\r<BR>\n" );
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